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JIMO is an international journal devoted to publishing peer-reviewed, high quality, original papers on the non-trivial interplay between numerical optimization methods and practically significant problems in industry or management so as to achieve superior design, planning and/or operation. Its objective is to promote collaboration between optimization specialists, industrial practitioners and management scientists so that important practical industrial and management problems can be addressed by the use of appropriate, recent advanced optimization techniques.

It is particularly hoped that the study of these practical problems will lead to the discovery of new ideas and the development of novel methodologies in optimization.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 4 issues a year in January, April, July and October.
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  • JIMO is published by the American Institute of Mathematical Sciences and sponsored by Curtin University and Zhejiang University. All rights reserved.


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A mixed-integer linear programming model for optimal vessel scheduling in offshore oil and gas operations
Elham Mardaneh  , Ryan Loxton  , Qun Lin  and  Phil Schmidli 
2017, 13(4) : 1601-1623 doi: 10.3934/jimo.2017009 +[Abstract](332) +[HTML](35) +[PDF](725.38KB)

This paper introduces a non-standard vehicle routing problem (VRP) arising in the oil and gas industry. The problem involves multiple offshore production facilities, each of which requires regular servicing by support vessels to replenish essential commodities such as food, water, fuel, and chemicals. The support vessels are also required to assist with oil off-takes, in which oil stored at a production facility is transported via hose to a waiting tanker. The problem is to schedule a series of round trips for the support vessels so that all servicing and off-take requirements are fulfilled, and total cost is minimized. Other constraints that must be considered include vessel suitability constraints (not every vessel is suitable for every facility), depot opening constraints (base servicing can only occur during specified opening periods), and off-take equipment constraints (the equipment needed for off-take support can only be deployed after certain commodities have been offloaded). Because of these additional constraints, the scheduling problem under consideration is far more difficult than the standard VRP. We formulate a mixed-integer linear programming (MILP) model for determining the optimal vessel schedule. We then verify the model theoretically and show how to compute the vessel utilization ratios for any feasible schedule. Finally, simulation results are reported for a real case study commissioned by Woodside Energy Ltd, Australia's largest dedicated oil and gas company.

On subspace properties of the quadratically constrained quadratic program
Xin Zhao  and  Jinyan Fan 
2017, 13(4) : 1625-1640 doi: 10.3934/jimo.2017010 +[Abstract](177) +[HTML](4) +[PDF](392.3KB)

In this paper, we study subspace properties of the quadratically constrained quadratic program (QCQP). We prove that, if an appropriate subspace is chosen to satisfy subspace properties, then the solution of the QCQP lies in that subspace. So, we can solve the QCQP in that subspace rather than solve it in the original space. The computational cost could be reduced significantly if the dimension of the subspace is much smaller. We also show how to construct such subspaces and investigate their dimensions.

Optimal pension decision under heterogeneous health statuses and bequest motives
Lin He  and  Zongxia Liang 
2017, 13(4) : 1641-1659 doi: 10.3934/jimo.2017011 +[Abstract](164) +[HTML](2) +[PDF](433.65KB)

In this paper, we study the optimal decision between ELA(Equity Linked Annuity) and ELID(Equity Linked Income Drawdown) pension plans under heterogeneous personal health statuses and bequest motives. In the ELA pension plan, the survival member receives the mortality credit, and leaves no bequest at the time of death, while the member receives no mortality credit and receives the fund wealth as bequest at the time of death in the ELID pension plan. The pension member controls the asset allocation and benefit outgo policies to achieve the objectives. We explore the square deviations between the actual benefit outgo and the pre-set target, and the square and negative linear deviations between the actual bequest and the pre-set target as the disutility function. The minimization of the disutility function is the objective of the stochastic optimal control problem. Using HJB (Hamilton-Jacobi-Bellman) equations and variational inequality methods, the closed-form optimal policies of the ELA and ELID pension plans are derived. Furthermore, the optimal decision boundary between the ELA and ELID plans is established. It is the first time to study the impacts of heterogeneous personal health status and bequest motive on the optimal choice between the ELA and ELID pension plans under the original performance criterions. The worse health status and higher bequest motive result in the higher utility of the ELID pension plan, and vice versa. The worse heath status increases the proportion allocated in the risky asset and increases the benefit outgo in both pension plans. The bequest motive has positive impacts on the proportion in the risky asset and negative impacts on the benefit outgo in the ELID pension plan.

Optimal ordering policy for a two-warehouse inventory model use of two-level trade credit
Jui-Jung Liao  , Wei-Chun Lee  , Kuo-Nan Huang  and  Yung-Fu Huang 
2017, 13(4) : 1661-1683 doi: 10.3934/jimo.2017012 +[Abstract](79) +[HTML](2) +[PDF](470.55KB)

In today's competitive markets, the supplier let the buyer to pay the purchasing cost after receiving the items, this strategy motivates the retailer to buy more items from the supplier and gains some benefit from the money which they did not pay at the time of receiving of the items. However, the retailer will be unable to pay off the debt obligations to the supplier in the future, so this study extends Yen et al. (2012) to consider the above situation and assumes the retailer can either pay off all accounts at the end of the delay period or delay incurring interest charges on the unpaid and overdue balance due to the difference between interest earned and interest charged. We will discuss the explorations of the function behaviors of the objection function to demonstrate the retailer's optimal replenishment cycle time not only exists but also is unique. Finally, numerical examples are given to illustrate the theorems and gained managerial insights.

Continuity of approximate solution maps to vector equilibrium problems
Lam Quoc Anh  , Pham Thanh Duoc  and  Tran Ngoc Tam 
2017, 13(4) : 1685-1699 doi: 10.3934/jimo.2017013 +[Abstract](204) +[HTML](2) +[PDF](367.2KB)

This paper considers the parametric primal and dual vector equilibrium problems in locally convex Hausdorff topological vector spaces. Based on linear scalarization technique, we establish sufficient conditions for the continuity of approximate solution maps to these problems. As applications, some new results for vector optimization problem and vector variational inequality are derived. Our results are new and improve the existing ones in the literature.

Artificial intelligence combined with nonlinear optimization techniques and their application for yield curve optimization
Roya Soltani  , Seyed Jafar Sadjadi  and  Mona Rahnama 
2017, 13(4) : 1701-1721 doi: 10.3934/jimo.2017014 +[Abstract](253) +[HTML](0) +[PDF](493.35KB)

This study makes use of the artificial intelligence approaches combined with some nonlinear optimization techniques for optimization of a well-known problem in financial engineering called yield curve. Yield curve estimation plays an important role on making strategic investment decisions. In this paper, we use two well-known parsimonious estimation models, Nelson-Siegel and Extended Nelson-Siegel, for the yield curve estimation. The proposed models of this paper are formulated as continuous nonlinear optimization problems. The resulted models are then solved using some nonlinear optimization and meta-heuristic approaches. The optimization techniques include hybrid GPSO parallel trust region-dog leg, Hybrid GPSO parallel trust region-nearly exact, Hybrid GPSO parallel Levenberg-Marquardt and Hybrid genetic electromagnetism like algorithm. The proposed models of this paper are examined using some real-world data from the bank of England and the results are analyzed.

An extension of hybrid method without extrapolation step to equilibrium problems
Van Hieu Dang 
2017, 13(4) : 1723-1741 doi: 10.3934/jimo.2017015 +[Abstract](106) +[HTML](1) +[PDF](470.61KB)

In this paper, we introduce a new hybrid algorithm for solving equilibrium problems. The algorithm combines the generalized gradient-like projection method and the hybrid (outer approximation) method. In this algorithm, only one optimization program is solved at each iteration without any extra-step dealing with the feasible set like as in the hybrid extragradient method and the hybrid Armijo linesearch method. A specially constructed half-space in the hybrid method is the reason for the absence of an optimization program in the proposed algorithm. The strongly convergent theorem is established and several numerical experiments are implemented to illustrate the convergence of the algorithm and compare it with others.

Structure analysis on the k-error linear complexity for 2n-periodic binary sequences
Jianqin Zhou  , Wanquan Liu  and  Xifeng Wang 
2017, 13(4) : 1743-1757 doi: 10.3934/jimo.2017016 +[Abstract](57) +[HTML](6) +[PDF](400.39KB)

In this paper, in order to characterize the critical error linear complexity spectrum (CELCS) for \begin{document}$2^n$\end{document}-periodic binary sequences, we first propose a decomposition based on the cube theory. Based on the proposed \begin{document}$k$\end{document}-error cube decomposition, and the famous inclusion-exclusion principle, we obtain the complete characterization of the \begin{document}$i$\end{document}th descent point (critical point) of the k-error linear complexity for \begin{document}$i=2,3$\end{document}. In fact, the proposed constructive approach has the potential to be used for constructing \begin{document}$2^n$\end{document}-periodic binary sequences with the given linear complexity and \begin{document}$k$\end{document}-error linear complexity (or CELCS), which is a challenging problem to be deserved for further investigation in future.

Minimization of the coefficient of variation for patient waiting system governed by a generic maximum waiting policy
Fanwen Meng  , Kiok Liang Teow  , Chee Kheong Ooi  , Bee Hoon Heng  and  Seow Yian Tay 
2017, 13(4) : 1759-1770 doi: 10.3934/jimo.2017017 +[Abstract](175) +[HTML](0) +[PDF](368.52KB)

Timely access of care has been widely recognized as an important dimension of health care quality. Waiting times can affect patient satisfaction and quality of care in the emergency department (ED). This study analyzes a general patient waiting policy such that ED patients who wait beyond a threshold have their wait shortened. Assuming that the policy is implemented to accelerate the long-waiting cases within a short time interval, we transform the original waiting distribution to a piecewise distribution. The objective of this paper is to examine the reliability of the induced waiting system by minimizing the coefficient of variation (CV) of waiting time. We convert the CV minimization problem to an approximation counterpart using the sampling technique. With patient waiting time data from an emergency department in Singapore, we derive the optimal values of parameters, such as the threshold and the length of the underlying time interval, needed in the policy. Numerical results show that CV and variance of new waiting time will be reduced remarkably by 38% and 58% respectively, in comparison with the original ones.

Minimizing expected time to reach a given capital level before ruin
Xiaoqing Liang  and  Lihua Bai 
2017, 13(4) : 1771-1791 doi: 10.3934/jimo.2017018 +[Abstract](127) +[HTML](1) +[PDF](563.4KB)

In this paper, we consider the optimal investment and reinsurance problem for an insurance company where the claim process follows a Brownian motion with drift. The insurer can purchase proportional reinsurance and invest its surplus in one risky asset and one risk-free asset. The goal of the insurance company is to minimize the expected time to reach a given capital level before ruin. By using the Hamilton-Jacobi-Bellman equation approach, we obtain explicit expressions for the value function and the optimal strategy. We also provide some numerical examples to illustrate the results obtained in this paper, and analyze the sensitivity of the parameters.

A numerical scheme for pricing American options with transaction costs under a jump diffusion process
Donny Citra Lesmana  and  Song Wang 
2017, 13(4) : 1793-1813 doi: 10.3934/jimo.2017019 +[Abstract](174) +[HTML](0) +[PDF](565.47KB)

In this paper we develop a numerical method for a nonlinear partial integro-differential complementarity problem arising from pricing American options with transaction costs when the underlying assets follow a jump diffusion process. We first approximate the complementarity problem by a nonlinear partial integro-differential equation (PIDE) using a penalty approach. The PIDE is then discretized by a combination of a spatial upwind finite differencing and a fully implicit time stepping scheme. We prove that the coefficient matrix of the system from this scheme is an M-matrix and that the approximate solution converges to the viscosity solution to the PIDE by showing that the scheme is consistent, monotone, and unconditionally stable. We also propose a Newton's iterative method coupled with a Fast Fourier Transform for the computation of the discretized integral term for solving the fully discretized system. Numerical results will be presented to demonstrate the convergence rates and usefulness of this method.

An uncertain wage contract model for risk-averse worker under bilateral moral hazard
Xiulan Wang  , Yanfei Lan  and  Wansheng Tang 
2017, 13(4) : 1815-1840 doi: 10.3934/jimo.2017020 +[Abstract](88) +[HTML](0) +[PDF](458.14KB)

This paper investigates a wage mechanism design problem faced by a risk neutral firm (he) who employs a risk averse worker (she) to sell products for him. The effort levels of both the firm and the worker are unobservable to each other, which results in bilateral moral hazard. The firm offers a wage contract menu to the worker with the objective of maximizing his expected profit. The results show that the firm will provide the same wage contract to the worker when the worker's effort is observable regardless of the market condition being full or private information. The optimal wage contract is related to the worker's risk averse level when the bilateral moral hazard exists. The information values of the worker's effort and the market condition are studied, respectively. The results show that the firm benefits from the worker's observable effort under full information and only when the sales uncertainty is sufficiently low, can the firm profit from that under private information. Moreover, only if the cost coefficient of the firm's effort is sufficiently high, the firm can benefit from full information in the scenario when the worker's effort is unobservable.

Incremental gradient-free method for nonsmooth distributed optimization
Jueyou Li  , Guoquan Li  , Zhiyou Wu  , Changzhi Wu  , Xiangyu Wang  , Jae-Myung Lee  and  Kwang-Hyo Jung 
2017, 13(4) : 1841-1857 doi: 10.3934/jimo.2017021 +[Abstract](128) +[HTML](4) +[PDF](457.57KB)

In this paper we consider the minimization of the sum of local convex component functions distributed over a multi-agent network. We first extend the Nesterov's random gradient-free method to the incremental setting. Then we propose the incremental gradient-free methods, including a cyclic order and a randomized order in the selection of component function. We provide the convergence and iteration complexity analysis of the proposed methods under some suitable stepsize rules. To illustrate our proposed methods, extensive numerical results on a distributed $l_1$-regression problem are presented. Compared with existing incremental subgradient-based methods, our methods only require the evaluation of the function values rather than subgradients, which may be preferred by practical engineers.

Non-convex semi-infinite min-max optimization with noncompact sets
Meixia Li  , Changyu Wang  and  Biao Qu 
2017, 13(4) : 1859-1881 doi: 10.3934/jimo.2017022 +[Abstract](192) +[HTML](0) +[PDF](468.2KB)

In this paper, first we study the non-convex sup-type functions with noncompact sets. Under quite mild conditions, the expressions of its derivative and subderivative along arbitrary direction are given. Furthermore, the structure of its subdifferential is characterized completely. Then, using these results, we establish first-order optimality conditions for semi-infinite min-max optimization problems. These results generalize and improve the corresponding results in the relevant literatures.

A new analytical model for optimized cognitive radio networks based on stochastic geometry
Seunghee Lee  and  Ganguk Hwang 
2017, 13(4) : 1883-1899 doi: 10.3934/jimo.2017023 +[Abstract](143) +[HTML](2) +[PDF](440.84KB)

In this paper, we consider an underlay type cognitive radio network with multiple secondary users who contend to access multiple heterogeneous licensed channels. With the help of stochastic geometry we develop a new analytical model to analyze a random channel access protocol where each secondary user determines whether to access a licensed channel based on a given access probability. In our analysis we introduce the so-called interference-free region to derive the coverage probability for an arbitrary secondary user. With the help of the interference-free region we approximate the interferences at an arbitrary secondary user from primary users as well as from secondary users in a simple way. Based on our analytical model we obtain the optimal access probabilities that maximize the throughput. Numerical examples are provided to validate our analysis.

Analysis of a discrete-time queue with general service demands and phase-type service capacities
Michiel De Muynck  , Herwig Bruneel  and  Sabine Wittevrongel 
2017, 13(4) : 1901-1926 doi: 10.3934/jimo.2017024 +[Abstract](90) +[HTML](2) +[PDF](540.38KB)

In this paper, we analyze a non-classical discrete-time queueing model where customers demand variable amounts of work from a server that is able to perform this work at a varying rate. The service demands of the customers are integer numbers of work units. They are assumed to be independent and identically distributed (i.i.d.) random variables. The service capacities, i.e., the numbers of work units that the server can process in the consecutive slots, are also assumed to be i.i.d. and their common probability generating function (pgf) is assumed to be rational. New customers arrive in the queueing system according to a general independent arrival process. For this queueing model we present an analysis method, which is based on complex contour integration. Expressions are obtained for the pgfs, the mean values and the tail probabilities of the customer delay and the system content in steady state. The analysis is illustrated by means of some numerical examples.

Single server retrial queues with speed scaling: analysis and performance evaluation
Tuan Phung-Duc  , Wouter Rogiest  and  Sabine Wittevrongel 
2017, 13(4) : 1927-1943 doi: 10.3934/jimo.2017025 +[Abstract](84) +[HTML](0) +[PDF](449.82KB)

Recently, queues with speed scaling have received considerable attention due to their applicability to data centers, enabling a better balance between performance and energy consumption. This paper proposes a new model where blocked customers must leave the service area and retry after a random time, with retrial rate either varying proportionally to the number of retrying customers (linear retrial rate) or non-varying (constant retrial rate). For both, we first study a basic case and then subsequently incorporate the concepts of a setup time and a deactivation time in extended versions of the model. In all cases, we obtain a full characterization of the stationary queue length distribution. This allows us to evaluate the performance in terms of the mentioned balance between performance and energy, using an existing cost function as well as a newly proposed variant thereof. This paper presents the derivation of the stationary distribution as well as several numerical examples of the cost-based performance evaluation.

Unified and refined analysis of the response time and waiting time in the M/M/m FCFS preemptive-resume priority queue
Hideaki Takagi 
2017, 13(4) : 1945-1973 doi: 10.3934/jimo.2017026 +[Abstract](252) +[HTML](2) +[PDF](339.9KB)

We present a unified and refined analysis of the response time and waiting time in the M/M/$ m $ FCFS preemptive-resume priority queueing system in the steady state by scrutinizing and extending the previous studies such as Brosh (1969), Segal (1970), Buzen and Bondi (1983), Tatashev (1984), and Zeltyn et al. (2009). In particular, we analyze the durations of interleaving waiting times and service times during the response time of a tagged customer of each priority class that is preempted by the arrivals of higher-priority class customers. Our new contribution includes the explicit formulas for the second and third moments of the response time and the third moment of the waiting time. We also clarify the dependence between the waiting time and the total service time. Numerical examples are shown in order to demonstrate the computation of theoretical formulas.

An integrated inventory model with variable transportation cost, two-stage inspection, and defective items
Biswajit Sarkar  , Bijoy Kumar Shaw  , Taebok Kim  , Sarkar Mitali  and  Dongmin Shin 
2017, 13(4) : 1975-1990 doi: 10.3934/jimo.2017027 +[Abstract](171) +[HTML](0) +[PDF](1170.2KB)

The paper deals with an integrated inventory model with make-to-order policy from buyer to vendor. A variable transportation cost is used as a power function of the delivery quantity for either tapering or considering proportional rate data to maintain single-setup multi-delivery (SSMD) policy with reduced transportation cost. A two-stage inspection process is introduced by the vendor to ensure the perfect quality of product even though the first inspection process indicates a constant defective rate of imperfect production is present during the long-run production system and all defective items are reworked with some fixed cost. The aim is to minimize the total cost of the integrated inventory model by using classical optimization technique. Two numerical examples, sensitivity analysis, and graphical representations are given to illustrate the model.

Prox-dual regularization algorithm for generalized fractional programs
Mostafa El Haffari  and  Ahmed Roubi 
2017, 13(4) : 1991-2013 doi: 10.3934/jimo.2017028 +[Abstract](80) +[HTML](3) +[PDF](429.8KB)

Prox-regularization algorithms for solving generalized fractional programs (GFP) were already considered by several authors. Since the standard dual of a generalized fractional program has not generally the form of GFP, these approaches can not apply directly to the dual problem. In this paper, we propose a primal-dual algorithm for solving convex generalized fractional programs. That is, we use a prox-regularization method to the dual problem that generates a sequence of auxiliary dual problems with unique solutions. So we can avoid the numerical difficulties that can occur if the fractional program does not have a unique solution. Our algorithm is based on Dinkelbach-type algorithms for generalized fractional programming, but uses a regularized parametric auxiliary problem. We establish then the convergence and rate of convergence of this new algorithm.

An efficient Tabu Search neighborhood based on reconstruction strategy to solve the blocking job shop scheduling problem
Adel Dabah  , Ahcene Bendjoudi  and  Abdelhakim AitZai 
2017, 13(4) : 2015-2031 doi: 10.3934/jimo.2017029 +[Abstract](192) +[HTML](10) +[PDF](484.69KB)

The blocking job shop scheduling problem (BJSS) is a version of the classical job shop scheduling with no intermediate buffer between machines. The BJSS is known to be NP-hard in the strong sense. A known way to solve such a problem is to use the Tabu Search algorithm (TS) which is a higher level heuristic procedure for solving optimization problems, designed to guide other methods to escape the trap of local optimality. However, the use of the classical TS neighborhood on BJSS problem produces infeasible solutions in most cases (98% of cases). This leads to waste valuable time in exploring infeasible solutions. To overcome this drawback, we propose a new tabu search neighborhood based on reconstruction strategy. This neighborhood consists to remove arcs causing the infeasibility and rebuild the neighbor solutions by using heuristics. Experiments on the reference benchmark instances show that the TS algorithm using the proposed neighborhood improves most of the known results in the literature and gives new upper bounds for more than 52 benchmarks in both BJSS cases (BJSS with Swap and BJSS no-Swap). Moreover, the proposed approach reaches much faster the optimal solution for most of the optimally solved benchmarks.

Stability strategies of manufacturing-inventory systems with unknown time-varying demand
Lizhao Yan  , Fei Xu  , Yongzeng Lai  and  Mingyong Lai 
2017, 13(4) : 2033-2047 doi: 10.3934/jimo.2017030 +[Abstract](154) +[HTML](3) +[PDF](529.4KB)

For a manufacturing-inventory system, its stability and robustness are of particular important. In the literature, most manufacturing-inventory models are constructed based on deterministic demand assumption. However, demands for many real-world manufacturing-inventory systems are non-deterministic. To minimize the gap between theory and practice, we construct two models for the inventory control problem involving multi-machine and multi-product manufacturing-inventory systems with uncertain time-varying demand, where physical decay rate and shelf life are accounted for in the models. We then design state feedback control strategies to stabilize such systems. Based on the Lyapunov stability theory, sufficient conditions for robust stability, stabilization and control are derived in the form of linear matrix inequalities. Numerical examples are presented to show the potential applications of the proposed models.

A cooperative game with envy
Jiahua Zhang  , Shu-Cherng Fang  , Yifan Xu  and  Ziteng Wang 
2017, 13(4) : 2049-2066 doi: 10.3934/jimo.2017031 +[Abstract](80) +[HTML](1) +[PDF](413.15KB)

This paper proposes an envy-incorporated cooperative game model and investigates the envy effects on players' coalition-forming and payoff-allocating decisions. A player's utility depends on her/his own payoff and the envy toward other players, inside and outside the same coalition, with higher payoffs. Envy core is defined to characterize stable coalition structures and payoff allocations of this new game. Conditions for the envy core to be nonempty are provided. The relative significance of in-coalition envy and out-coalition envy is shown to be a key factor to the form of the envy core. Application to a simple game shows that envy may significantly change players' decisions.

Comparison of GA and PSO approaches for the direct and LQR tuning of a multirotor PD controller
Valeria Artale  , Cristina L. R. Milazzo  , Calogero Orlando  and  Angela Ricciardello 
2017, 13(4) : 2067-2091 doi: 10.3934/jimo.2017032 +[Abstract](251) +[HTML](0) +[PDF](2891.44KB)

In the present paper different approaches for flight control stabilization tuning of a prototype of Unmanned Aerial Vehicle (UAV) are investigated. The mathematical model of a multirotor airframe is presented and its dynamical system is described by means of Newton-Euler equations for a rigid body. The proposed controller systems for the stabilization of the altitude and the attitude of the multirotor around its hovering configuration are based on Proportional Derivative (PD) regulator tuned by optimization techniques such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) or, for the linearized system, by means of Linear Quadratic Regulator (LQR). In this case, PSO and GA are applied to set entries of LQR scheme. Control flight simulation results have been compared in terms of minimization of work carried out by the control actions. Performed simulations pointed out that all approaches lead to zero the error of the position along gravity acceleration direction, stop the rotation of UAV around body axes and stabilize the multirotor. The direct PSO tuning of the PD parameters (PD-PSO) shows better results in terms of errors, performance and speed of convergence.

Light-tailed asymptotics of GI/G/1-type Markov chains
Tatsuaki Kimura  , Hiroyuki Masuyama  and  Yutaka Takahashi 
2017, 13(4) : 2093-2146 doi: 10.3934/jimo.2017033 +[Abstract](157) +[HTML](4) +[PDF](831.2KB)

This paper studies the light-tailed asymptotics of the stationary distribution of the GI/G/1-type Markov chain. We consider three cases:(ⅰ) the tail decay rate is determined by a certain parameter \begin{document}$\theta$\end{document} associated with the transition block matrices \begin{document}$\{\boldsymbol{A}(k);k=0,\pm1,\pm2,\dots\}$\end{document} in the non-boundary levels; (ⅱ) by the convergence radius of the generating function of the transition block matrices \begin{document}$\{\boldsymbol{B}(k);k=1,2,\dots\}$\end{document} in the boundary level; and (ⅲ) by the convergence radius of \begin{document}$\sum_{k=1}^{\infty}z^k \boldsymbol{A}(k)$\end{document}. In the case (ⅰ), we extend the existing asymptotic formula for the M/G/1-type Markov chain to the GI/G/1-type one. In the case (ⅱ), we present general asymptotic formulas that include, as special cases, the existing results in the literature. In the case (ⅲ), we derive new asymptotic formulas. As far as we know, such formulas have not been reported in the literature.

The optimal cash holding models for stochastic cash management of continuous time
Zhengyan Wang  , Guanghua Xu  , Peibiao Zhao  and  Zudi Lu 
2017doi: 10.3934/jimo.2017034 +[Abstract](184) +[HTML](28) +[PDF](483.19KB)
$\mathcal{H}_\infty$ filtering for switched nonlinear systems: A state projection method
Lin Du  and  Yun Zhang 
2017doi: 10.3934/jimo.2017035 +[Abstract](56) +[HTML](17) +[PDF](492.58KB)
A note on a Lévy insurance risk model under periodic dividend decisions
Zhimin Zhang  and  Eric C. K. Cheung 
2017doi: 10.3934/jimo.2017036 +[Abstract](58) +[HTML](24) +[PDF](437.68KB)
Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems
Lam Quoc Anh  and  Nguyen Van Hung 
2017doi: 10.3934/jimo.2017037 +[Abstract](141) +[HTML](34) +[PDF](370.9KB)
Modeling and computation of water management by real options
Shuhua Zhang  , Xinyu Wang  and  Hua Li 
2017doi: 10.3934/jimo.2017038 +[Abstract](159) +[HTML](22) +[PDF](1706.22KB)
Advertising games on national brand and store brand in a dual-channel supply chain
Lei Yang  , Jingna Ji  and  Kebing Chen 
2017doi: 10.3934/jimo.2017039 +[Abstract](122) +[HTML](23) +[PDF](504.8KB)
Joint decision on pricing and waste emission level in industrial symbiosis chain
Binbin Cao  , Zhongdong Xiao  and  Xiaojun Li 
2017doi: 10.3934/jimo.2017040 +[Abstract](175) +[HTML](9) +[PDF](631.7KB)
Integrated order acceptance and scheduling decision making in product service supply chain with hard time windows constraints
Bin Dan  , Huali Gao  , Yang Zhang  , Ru Liu  and  Songxuan Ma 
2017doi: 10.3934/jimo.2017041 +[Abstract](139) +[HTML](23) +[PDF](367.78KB)
Optimal control of switched systems with multiple time-delays and a cost on changing control
Zhaohua Gong  , Chongyang Liu  and  Yujing Wang 
2017doi: 10.3934/jimo.2017042 +[Abstract](87) +[HTML](18) +[PDF](313.56KB)
Neutral and indifference pricing with stochastic correlation and volatility
Jia Yue  and  Nan-Jing Huang 
2017doi: 10.3934/jimo.2017043 +[Abstract](94) +[HTML](17) +[PDF](498.17KB)
Asymptotics for ruin probabilities in Lévy-driven risk models with heavy-tailed claims
Yang Yang  , Kam C. Yuen  and  Jun-Feng Liu 
2017doi: 10.3934/jimo.2017044 +[Abstract](136) +[HTML](12) +[PDF](398.9KB)
A mean-field formulation for multi-period asset-liability mean-variance portfolio selection with probability constraints
Xianping Wu  , Xun Li  and  Zhongfei Li 
2017doi: 10.3934/jimo.2017045 +[Abstract](77) +[HTML](17) +[PDF](348.41KB)
Optimal production run time and inspection errors in an imperfect production system with warranty
Biswajit Sarkar  , Bimal Kumar Sett  and  Sumon Sarkar 
2017doi: 10.3934/jimo.2017046 +[Abstract](108) +[HTML](16) +[PDF](729.0KB)
Some robust improved geometric aggregation operators under interval-valued intuitionistic fuzzy environment for multi-criteria decision-making process
Harish Garg 
2017doi: 10.3934/jimo.2017047 +[Abstract](173) +[HTML](18) +[PDF](489.1KB)
On analyzing and detecting multiple optima of portfolio optimization
Yue Qi  , ZhiHao Wang  and  Su Zhang 
2017doi: 10.3934/jimo.2017048 +[Abstract](57) +[HTML](17) +[PDF](448.3KB)
Is social responsibility for firms competing on quantity evolutionary stable?
Caichun Chai  , Tiaojun Xiao  and  Eilin Francis 
2017doi: 10.3934/jimo.2017049 +[Abstract](76) +[HTML](16) +[PDF](3156.4KB)
Pricing and ordering strategies of supply chain with selling gift cards
Jingming Pan  , Wenqing Shi  and  Xiaowo Tang 
2017doi: 10.3934/jimo.2017050 +[Abstract](58) +[HTML](16) +[PDF](1891.0KB)
Optimal dividend and capital injection strategy with excess-of-loss reinsurance and transaction costs
Gongpin Cheng  , Rongming Wang  and  Dingjun Yao 
2017doi: 10.3934/jimo.2017051 +[Abstract](45) +[HTML](16) +[PDF](438.1KB)
A modified strictly contractive Peaceman-Rachford splitting method for multi-block separable convex programming
Su-Hong Jiang  and  Min Li 
2017doi: 10.3934/jimo.2017052 +[Abstract](77) +[HTML](19) +[PDF](462.0KB)
An iterative algorithm for periodic Sylvester matrix equations
Lingling Lv  , Zhe Zhang  , Lei Zhang  and  Weishu Wang 
2017doi: 10.3934/jimo.2017053 +[Abstract](70) +[HTML](18) +[PDF](178.1KB)
Ebola model and optimal control with vaccination constraints
Iván Area  , Faïçal Ndaïrou  , Juan J. Nieto  , Cristiana J. Silva  and  Delfim F. M. Torres 
2017doi: 10.3934/jimo.2017054 +[Abstract](264) +[HTML](18) +[PDF](893.6KB)
The multimodal and multiperiod urban transportation integrated timetable construction problem with demand uncertainty
Paulina Ávila-Torres  , Fernando López-Irarragorri  , Rafael Caballero  and  Yasmín Ríos-Solís 
2017doi: 10.3934/jimo.2017055 +[Abstract](47) +[HTML](14) +[PDF](1243.8KB)
Optimal control of a parabolic distributed parameter system using a fully exponentially convergent barycentric shifted Gegenbauer integral pseudospectral method
Kareem T. Elgindy 
2017doi: 10.3934/jimo.2017056 +[Abstract](80) +[HTML](16) +[PDF](558.1KB)
An improved 2.11-competitive algorithm for online scheduling on parallel machines to minimize total weighted completion time
Ran Ma  and  Jiping Tao 
2017doi: 10.3934/jimo.2017057 +[Abstract](55) +[HTML](17) +[PDF](356.5KB)
Integrated recycling-production-distribution planning for decentralized closed-loop supply chain
Yi Jing  and  Wenchuan Li 
2017doi: 10.3934/jimo.2017058 +[Abstract](152) +[HTML](17) +[PDF](478.0KB)
Sparse Markowitz portfolio selection by using stochastic linear complementarity approach
Qiyu Wang  and  Hailin Sun 
2017doi: 10.3934/jimo.2017059 +[Abstract](63) +[HTML](19) +[PDF](470.9KB)
Design of a single window system for e-government services: The Chilean case
Alejandro Cataldo  , Juan-Carlos Ferrer  , Pablo A. Rey  and  Antoine Sauré 
2017doi: 10.3934/jimo.2017060 +[Abstract](180) +[HTML](50) +[PDF](735.5KB)
LP approach to exponential stabilization of singular linear positive time-delay systems via memory state feedback
Nguyen H. Sau  and  Vu N. Phat 
2017doi: 10.3934/jimo.2017061 +[Abstract](244) +[HTML](18) +[PDF](348.4KB)
An optimized direction statistics for detecting and removing random-valued impulse noise
Hao Yang  , Hang Qiu  and  Leiting Chen 
2017doi: 10.3934/jimo.2017062 +[Abstract](125) +[HTML](20) +[PDF](1007.5KB)
D.C. programming approach for solving an applied ore-processing problem
R. Enkhbat  , T. V. Gruzdeva  and  M. V. Barkova 
2017doi: 10.3934/jimo.2017063 +[Abstract](85) +[HTML](14) +[PDF](301.5KB)
Globally solving quadratic programs with convex objective and complementarity constraints via completely positive programming
Zhi-Bin Deng  , Ye Tian  , Cheng Lu  and  Wen-Xun Xing 
2017doi: 10.3934/jimo.2017064 +[Abstract](49) +[HTML](19) +[PDF](346.0KB)
Solving normalized stationary points of a class of equilibrium problem with equilibrium constraints
Peiyu li 
2017doi: 10.3934/jimo.2017065 +[Abstract](40) +[HTML](10) +[PDF](306.5KB)
A study on institutional investors selecting better stocks: Evidence from SEOs in China
Rui Li  and  Shaoyong Lai 
2017doi: 10.3934/jimo.2017066 +[Abstract](94) +[HTML](17) +[PDF](244.3KB)
Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer
Yan Wang  , Yanxiang Zhao  , Lei Wang  , Aimin Song  and  Yanping Ma 
2017doi: 10.3934/jimo.2017067 +[Abstract](177) +[HTML](18) +[PDF](444.5KB)
Lyapunov method for stability of descriptor second-order and high-order systems
Guoshan Zhang  and  Peizhao Yu 
2017doi: 10.3934/jimo.2017068 +[Abstract](77) +[HTML](21) +[PDF](404.4KB)
A loss-averse two-product ordering model with information updating in two-echelon inventory system
Yanju Zhou  , Zhen Shen  , Renren Ying  and  Xuanhua Xu 
2017doi: 10.3934/jimo.2017069 +[Abstract](52) +[HTML](21) +[PDF](362.2KB)
An adaptive trust region algorithm for large-residual nonsmooth least squares problems
Zhou Sheng  , Gonglin Yuan  , Zengru Cui  , Xiabin Duan  and  Xiaoliang Wang 
2017doi: 10.3934/jimo.2017070 +[Abstract](129) +[HTML](15) +[PDF](191.7KB)
Least absolute deviations learning of multiple tasks
Wei Xue  , Wensheng Zhang  and  Gaohang Yu 
2017doi: 10.3934/jimo.2017071 +[Abstract](54) +[HTML](29) +[PDF](509.6KB)
A stochastic newsvendor game with dynamic retail prices
Ido Polak  and  Nicolas Privault 
2017doi: 10.3934/jimo.2017072 +[Abstract](224) +[HTML](14) +[PDF](414.4KB)
Analysis of a batch service multi-server polling system with dynamic service control
Tao Jiang  and  Liwei Liu 
2017doi: 10.3934/jimo.2017073 +[Abstract](84) +[HTML](17) +[PDF](357.4KB)
Dispersion with connectivity in wireless mesh networks
Birol Yüceoğlu  , Ş. İlker Birbil  and  Özgür Gürbüz 
2017doi: 10.3934/jimo.2017074 +[Abstract](305) +[HTML](13) +[PDF](681.8KB)
A modified scaled memoryless BFGS preconditioned conjugate gradient algorithm for nonsmooth convex optimization
Yigui Ou  and  Xin Zhou 
2017doi: 10.3934/jimo.2017075 +[Abstract](161) +[HTML](17) +[PDF](405.7KB)
Multi-machine scheduling with interval constrained position-dependent processing times
Xianyu Yu  , Dar-Li Yang  , Dequn Zhou  and  Peng Zhou 
2017doi: 10.3934/jimo.2017076 +[Abstract](94) +[HTML](17) +[PDF](314.4KB)
Parameter identification techniques applied to an environmental pollution model
Yuepeng Wang  , Yue Cheng  , I. Michael Navon  and  Yuanhong Guan 
2017doi: 10.3934/jimo.2017077 +[Abstract](229) +[HTML](22) +[PDF](407.7KB)
Linearized block-wise alternating direction method of multipliers for multiple-block convex programming
Zhongming Wu 
2017doi: 10.3934/jimo.2017078 +[Abstract](63) +[HTML](24) +[PDF](2327.9KB)
Ergodic control for a mean reverting inventory model
Jingzhen Liu  , Ka Fai Cedric Yiu  and  Alain Bensoussan 
2017doi: 10.3934/jimo.2017079 +[Abstract](107) +[HTML](20) +[PDF](448.4KB)
Optimal production schedule in a single-supplier multi-manufacturer supply chain involving time delays in both levels
Kar Hung Wong  , Yu Chung Eugene Lee  , Heung Wing Joseph Lee  and  Chi Kin Chan 
2017doi: 10.3934/jimo.2017080 +[Abstract](28) +[HTML](19) +[PDF](499.4KB)
On optimality conditions and duality for non-differentiable interval-valued programming problems with the generalized $(F,\rho)$-convexity
Xiuhong Chen  and  Zhihua Li 
2017doi: 10.3934/jimo.2017081 +[Abstract](52) +[HTML](17) +[PDF](364.7KB)
Indefinite LQ optimal control with process state inequality constraints for discrete-time uncertain systems
Yuefen Chen  and  Yuanguo Zhu 
2017doi: 10.3934/jimo.2017082 +[Abstract](126) +[HTML](13) +[PDF](416.8KB)
Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts
Shouyu Ma  , Zied jemai  , Evren Sahin  and  Yves Dallery 
2017doi: 10.3934/jimo.2017083 +[Abstract](45) +[HTML](20) +[PDF](587.2KB)
Solutions for bargaining games with incomplete information: General type space and action space
Feimin Zhong  , Jinxing Xie  and  Jing Jiao 
2017doi: 10.3934/jimo.2017084 +[Abstract](216) +[HTML](21) +[PDF](341.3KB)
Single-machine rescheduling problems with learning effect under disruptions
Mingbao Cheng  , Shuxian Xiao  and  Guosheng Liu 
2017doi: 10.3934/jimo.2017085 +[Abstract](164) +[HTML](19) +[PDF](329.4KB)
On the convergence properties of a smoothing approach for mathematical programs with symmetric cone complementarity constraints
Yi Zhang  , Liwei Zhang  and  Jia Wu 
2017doi: 10.3934/jimo.2017086 +[Abstract](50) +[HTML](98) +[PDF](525.6KB)
Uniqueness of solutions to fuzzy relational equations regarding Max-av composition and strong regularity of the matrices in Max-av algebra
Jun Xie  , Jinlong Yuan  , Dongxia Wang  , Weili Liu  and  Chongyang Liu 
2017doi: 10.3934/jimo.2017087 +[Abstract](125) +[HTML](16) +[PDF](345.9KB)
Optimal decisions for a dual-channel supply chain under information asymmetry
Mingyong Lai  , Hongzhao Yang  , Erbao Cao  , Duo Qiu  and  Jing Qiu 
2017doi: 10.3934/jimo.2017088 +[Abstract](139) +[HTML](48) +[PDF](548.9KB)
Second-order optimality conditions for cone constrained multi-objective optimization
Liwei Zhang  , Jihong Zhang  and  Yule Zhang 
2017doi: 10.3934/jimo.2017089 +[Abstract](116) +[HTML](18) +[PDF](406.7KB)
Optimal risk control and dividend strategies in the presence of two reinsurers: Variance premium principle
Dingjun Yao  and  Kun Fan 
2017doi: 10.3934/jimo.2017090 +[Abstract](55) +[HTML](20) +[PDF](538.7KB)
A variational inequality approach for constrained multifacility Weber problem under gauge
Jianlin Jiang  , Shun Zhang  , Su Zhang  and  Jie Wen 
2017doi: 10.3934/jimo.2017091 +[Abstract](127) +[HTML](17) +[PDF](463.9KB)
Portfolio procurement policies for budget-constrained supply chains with option contracts and external financing
Benyong Hu  , Xu Chen  , Felix T. S. Chan  and  Chao Meng 
2017doi: 10.3934/jimo.2018001 +[Abstract](21) +[HTML](9) +[PDF](660.66KB)
Modeling and analyzing the chaotic behavior in supply chain networks: a control theoretic approach
Hamid Norouzi Nav  , Mohammad Reza Jahed Motlagh  and  Ahmad Makui 
2017doi: 10.3934/jimo.2018002 +[Abstract](11) +[HTML](7) +[PDF](447.7KB)
A new proximal chebychev center cutting plane algorithm for nonsmooth optimization and its convergence
Jie Shen  , Jian Lv  , Fang-Fang Guo  , Ya-Li Gao  and  Rui Zhao 
2017doi: 10.3934/jimo.2018003 +[Abstract](7) +[HTML](4) +[PDF](416.71KB)
Solving the interval-valued optimization problems based on the concept of null set
Hsien-Chung Wu 
2017doi: 10.3934/jimo.2018004 +[Abstract](13) +[HTML](3) +[PDF](353.61KB)
A threshold-based risk process with a waiting period to pay dividends
Steve Drekic  , Jae-Kyung Woo  and  Ran Xu 
2017doi: 10.3934/jimo.2018005 +[Abstract](10) +[HTML](3) +[PDF](650.24KB)
Competition of pricing and service investment between iot-based and traditional manufacturers
Zhiping Zhou  , Xinbao Liu  , Jun Pei  , Panos M. Pardalos  and  Hao Cheng 
2017doi: 10.3934/jimo.2018006 +[Abstract](30) +[HTML](18) +[PDF](568.58KB)
A performance comparison and evaluation of metaheuristics for a batch scheduling problem in a multi-hybrid cell manufacturing system with skilled workforce assignment
Omer Faruk Yilmaz  and  Mehmet Bulent Durmusoglu 
2017doi: 10.3934/jimo.2018007 +[Abstract](157) +[HTML](61) +[PDF](1155.74KB)
Strategic behavior and optimal strategies in an M/G/1 queue with Bernoulli vacations
Sheng Zhu  and  Jinting Wang 
2017doi: 10.3934/jimo.2018008 +[Abstract](28) +[HTML](23) +[PDF](576.12KB)
Optimal investment and dividend payment strategies with debt management and reinsurance
Qian Zhao  , Zhuo Jin  and  Jiaqin Wei 
2017doi: 10.3934/jimo.2018009 +[Abstract](9) +[HTML](5) +[PDF](406.3KB)
Modeling and computation of energy efficiency management with emission permits trading
Shuhua Zhang  , Xinyu Wang  and  Song Wang 
2017doi: 10.3934/jimo.2018010 +[Abstract](26) +[HTML](17) +[PDF](956.83KB)
Disaster relief routing in limited capacity road networks with heterogeneous flows
Linet Ozdamar  , Dilek Tuzun Aksu  , Elifcan Yasa  and  Biket Ergunes 
2017doi: 10.3934/jimo.2018011 +[Abstract](40) +[HTML](22) +[PDF](698.42KB)
A power penalty method for a class of linearly constrained variational inequality
Ming Chen  and  Chongchao Huang 
2017doi: 10.3934/jimo.2018012 +[Abstract](24) +[HTML](23) +[PDF](439.58KB)
Compensation plan, pricing and production decisions with inventory-dependent salvage value, and asymmetric risk-averse sales agent
Kegui Chen  , Xinyu Wang  , Min Huang  and  Wai-Ki Ching 
2017doi: 10.3934/jimo.2018013 +[Abstract](32) +[HTML](37) +[PDF](560.17KB)
Performance optimization of parallel-distributed processing with checkpointing for cloud environment
Tsuguhito Hirai  , Hiroyuki Masuyama  , Shoji Kasahara  and  Yutaka Takahashi 
2017doi: 10.3934/jimo.2018014 +[Abstract](28) +[HTML](35) +[PDF](421.67KB)
Optimal liability ratio and dividend payment strategies under catastrophic risk
Linyi Qian  , Lyu Chen  , Zhuo Jin  and  Rongming Wang 
2017doi: 10.3934/jimo.2018015 +[Abstract](33) +[HTML](25) +[PDF](463.38KB)
Parameter identification and numerical simulation for the exchange coefficient of dissolved oxygen concentration under ice in a boreal lake
Qinxi Bai  , Zhijun Li  , Lei Wang  , Bing Tan  and  Enmin Feng 
2017doi: 10.3934/jimo.2018016 +[Abstract](44) +[HTML](25) +[PDF](2785.48KB)
Scheduling family jobs on an unbounded parallel-batch machine to minimize makespan and maximum flow time
Zhichao Geng  and  Jinjiang Yuan 
2017doi: 10.3934/jimo.2018017 +[Abstract](20) +[HTML](30) +[PDF](336.92KB)
Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process
Harish Garg 
2017doi: 10.3934/jimo.2018018 +[Abstract](32) +[HTML](18) +[PDF](430.25KB)
Optimal pricing and inventory management for a loss averse firm when facing strategic customers
Ruopeng Wang  , Jinting Wang  and  Chang Sun 
2017doi: 10.3934/jimo.2018019 +[Abstract](40) +[HTML](36) +[PDF](500.75KB)
Analysis of a dynamic premium strategy: From theoretical and marketing perspectives
Wing Yan Lee  and  Fangda Liu 
2017doi: 10.3934/jimo.2018020 +[Abstract](6) +[HTML](9) +[PDF](386.0KB)
Frequency $H_{2}/H_{∞}$ optimizing control for isolated microgrid based on IPSO algorithm
Zhong-Qiang Wu  and  Xi-Bo Zhao 
2017doi: 10.3934/jimo.2018021 +[Abstract](23) +[HTML](16) +[PDF](1111.93KB)
Adjoint-based parameter and state estimation in 1-D magnetohydrodynamic (MHD) flow system
Zhigang Ren  , Shan Guo  , Zhipeng Li  and  Zongze Wu 
2017doi: 10.3934/jimo.2018022 +[Abstract](33) +[HTML](27) +[PDF](998.36KB)
The modified inertial relaxed CQ algorithm for solving the split feasibility problems
Suthep Suantai  , Nattawut Pholasa  and  Prasit Cholamjiak 
2017doi: 10.3934/jimo.2018023 +[Abstract](32) +[HTML](22) +[PDF](454.66KB)
Tunneling behaviors of two mutual funds
Lin He  , Zongxia Liang  and  Xiaoyang Zhao 
2017doi: 10.3934/jimo.2018024 +[Abstract](21) +[HTML](35) +[PDF](1290.14KB)
A generalized approach to sparse and stable portfolio optimization problem
Zhifeng Dai  and  Fenghua Wen 
2017doi: 10.3934/jimo.2018025 +[Abstract](30) +[HTML](24) +[PDF](378.08KB)
Selective void creation/filling for variable size packets and multiple wavelengths
Kurt Van Hautegem  , Wouter Rogiest  and  Herwig Bruneel 
2017doi: 10.3934/jimo.2018026 +[Abstract](30) +[HTML](20) +[PDF](3994.36KB)
Integrated supply chain design models: a survey and future research directions
Zuo-Jun max Shen 
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The control parameterization method for nonlinear optimal control: A survey
Qun Lin  , Ryan Loxton  and  Kok Lay Teo 
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New adaptive stepsize selections in gradient methods
Giacomo Frassoldati  , Luca Zanni  and  Gaetano Zanghirati 
2008, 4(2) : 299-312 doi: 10.3934/jimo.2008.4.299 +[Abstract](45) +[PDF](201.3KB) Cited By(45)
A new exact penalty function method for continuous inequality constrained optimization problems
Changjun Yu  , Kok Lay Teo  , Liansheng Zhang  and  Yanqin Bai 
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Solutions and optimality criteria to box constrained nonconvex minimization problems
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Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture
Chongyang Liu  , Zhaohua Gong  , Enmin Feng  and  Hongchao Yin 
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A class of gap functions for quasi-variational inequality problems
Masao Fukushima 
2007, 3(2) : 165-171 doi: 10.3934/jimo.2007.3.165 +[Abstract](60) +[PDF](129.8KB) Cited By(35)
A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers
Bao Qing Hu  and  Song Wang 
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Fractional order optimal control problems with free terminal time
Shakoor Pooseh  , Ricardo Almeida  and  Delfim F. M. Torres 
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Solving structural engineering design optimization problems using an artificial bee colony algorithm
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Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems
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The optimal cash holding models for stochastic cash management of continuous time
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Selective void creation/filling for variable size packets and multiple wavelengths
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Competition of pricing and service investment between iot-based and traditional manufacturers
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Optimal decisions for a dual-channel supply chain under information asymmetry
Mingyong Lai  , Hongzhao Yang  , Erbao Cao  , Duo Qiu  and  Jing Qiu 
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Modeling and computation of water management by real options
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A note on a Lévy insurance risk model under periodic dividend decisions
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Performance optimization of parallel-distributed processing with checkpointing for cloud environment
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