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 2155-3289

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Volume 9, 2019

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Numerical Algebra, Control and Optimization (NACO) aims at publishing original papers on any non-trivial interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear algebraic systems. Topics of interest to NACO include the following: original research in theory, algorithms and applications of optimization; numerical methods for linear and nonlinear algebraic systems arising in modelling, control and optimisation; and original theoretical and applied research and development in the control of systems including all facets of control theory and its applications. In the application areas, special interests are on artificial intelligence and data sciences. The journal also welcomes expository submissions on subjects of current relevance to readers of the journal. The publication of papers in NACO is free of charge.

  • 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 March, June, September and December.
  • Publishes both online and in print.
  • Indexed in Scopus, MathSciNet, Zentralblatt MATH and Emerging Sources Citation Index.
  • Archived in Portico and CLOCKSS.
  • NACO is a publication of the American Institute of Mathematical Sciences. All rights reserved.

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Integrated modeling and optimization of material flow and financial flow of supply chain network considering financial ratios
Qiong Liu, Ahmad Reza Rezaei, Kuan Yew Wong and Mohammad Mahdi Azami
2019, 9(2) : 113-132 doi: 10.3934/naco.2019009 +[Abstract](209) +[HTML](70) +[PDF](445.67KB)
Abstract:

In today's competitive environment, businesses are searching for tools and instruments, using which they can reduce their costs as much as possible in order to increase profits. The supply chain as a process which requires comprehensive management can be a great help in this regard for companies. The majority of approaches evaluated in supply chain primarily deal with logistic and material flows and neglect a lot of financial dimensions. This is while the financial flow in the supply chain can play an effective role in improving and optimizing the chain and contribute heavily to the profitability of the business. This paper deals with the financial flow of the supply chain model along with the material flow. It indicates that while optimizing the financial flow will provide the maximum profit for the plant, through simultaneous modeling of both these flows, better results can be reached. On the other hand, optimizing the financial flow allows the financial factors to be also considered in the model, which helps the business reach higher profits and better management of financial processes, which in turn shifts the business towards a modern industrial unit.

Second order modified objective function method for twice differentiable vector optimization problems over cone constraints
Anurag Jayswala, Tadeusz Antczakb and Shalini Jha
2019, 9(2) : 133-145 doi: 10.3934/naco.2019010 +[Abstract](170) +[HTML](68) +[PDF](345.44KB)
Abstract:

In the paper, a vector optimization problem with twice differentiable functions and cone constraints is considered. The second order modified objective function method is used for solving such a multiobjective programming problem. In this method, for the considered twice differentiable multi-criteria optimization problem, its associated second order vector optimization problem with the modified objective function is constructed at the given arbitrary feasible solution. Then, the equivalence between the sets of (weakly) efficient solutions in the original twice differentiable vector optimization problem with cone constraints and its associated modified vector optimization problem is established. Further, the relationship between an (weakly) efficient solution in the original vector optimization problem and a saddle-point of the second order Lagrange function defined for the modified vector optimization problem is also analyzed.

A Mehrotra type predictor-corrector interior-point algorithm for linear programming
Soodabeh Asadi and Hossein Mansouri
2019, 9(2) : 147-156 doi: 10.3934/naco.2019011 +[Abstract](171) +[HTML](97) +[PDF](344.27KB)
Abstract:

In this paper, we analyze a feasible predictor-corrector linear programming variant of Mehrotra's algorithm. The analysis is done in the negative infinity neighborhood of the central path. We demonstrate the theoretical efficiency of this algorithm by showing its polynomial complexity. The complexity result establishes an improvement of factor \begin{document}$ n^3 $\end{document} in the theoretical complexity of an earlier presented variant in [2], which is a huge improvement. We examine the performance of our algorithm by comparing its implementation results to solve some NETLIB problems with the algorithm presented in [2].

A new reprojection of the conjugate directions
József Abaffy
2019, 9(2) : 157-171 doi: 10.3934/naco.2019012 +[Abstract](144) +[HTML](77) +[PDF](418.23KB)
Abstract:

In the paper we apply a Parlett–Kahan's "twice is enough" type algorithm to conjugate directions. We give a lower bound of the digits of precision of the conjugate directions, too.

Iterative methods for solving large sparse Lyapunov equations and application to model reduction of index 1 differential-algebraic-equations
M. Sumon Hossain and M. Monir Uddin
2019, 9(2) : 173-186 doi: 10.3934/naco.2019013 +[Abstract](169) +[HTML](85) +[PDF](487.85KB)
Abstract:

To implement the balancing based model reduction of large-scale dynamical systems we need to compute the low-rank (controllability and observability) Gramian factors by solving Lyapunov equations. In recent time, Rational Krylov Subspace Method (RKSM) is considered as one of the efficient methods for solving the Lyapunov equations of large-scale sparse dynamical systems. The method is well established for solving the Lyapunov equations of the standard or generalized state space systems. In this paper, we develop algorithms for solving the Lyapunov equations for large-sparse structured descriptor system of index-1. The resulting algorithm is applied for the balancing based model reduction of large sparse power system model. Numerical results are presented to show the efficiency and capability of the proposed algorithm.

Application of robust optimization for a product portfolio problem using an invasive weed optimization algorithm
Alireza Goli, Hasan Khademi Zare, Reza Tavakkoli-Moghaddam and Ahmad Sadeghieh
2019, 9(2) : 187-209 doi: 10.3934/naco.2019014 +[Abstract](204) +[HTML](70) +[PDF](1116.99KB)
Abstract:

Product portfolio optimization (PPO) is a strategic decision for many organizations. There are several technical methods for facilitating this decision. According to the reviewed studies, the implementation of the robust optimization approach and the invasive weed optimization (IWO) algorithm is the research gap in this field. The contribution of this paper is the development of the PPO problem with the help of the robust optimization approach and the multi-objective IWO algorithm. Considering the profit margin uncertainty in real-world investment decisions, the robust optimization approach is used to address this issue. To illustrate the real-world applicability of the model, it is implemented for dairy products of Pegah Golpayegan Company in Iran. The numerical results obtained from the IWO algorithm demonstrate the effectiveness of the proposed algorithm in tracing out the efficiency frontier of the product portfolio. The average risk of efficient frontier solutions in the deterministic model is about 0.4 and for the robust counterpart formulation is at least 0.5 per product. The efficient frontier solutions obtained from robust counterpart formulation demonstrate a more realistic risk level than the deterministic model. The comparisons between CPLEX, IWO and genetic algorithm (GA) shows that the performance of the IWO algorithm is much better than the older algorithms and can be considered as an alternative to algorithms, such as GA in product portfolio optimization problems.

Homotopy method for matrix rank minimization based on the matrix hard thresholding method
Zhengshan Dong, Jianli Chen and Wenxing Zhu
2019, 9(2) : 211-224 doi: 10.3934/naco.2019015 +[Abstract](138) +[HTML](81) +[PDF](375.08KB)
Abstract:

Based on the matrix hard thresholding method, a homotopy method is proposed for solving the matrix rank minimization problem. This method iteratively solves a series of regularization subproblems, whose solutions are given in closed form by the matrix hard thresholding operator. Under some mild assumptions, convergence of the proposed method is proved. The proposed method does not depend on a prior knowledge of exact rank value. Numerical experiments demonstrate that the proposed homotopy method weakens the affection of the choice of the regularization parameter, and is more efficient and effective than the existing sate-of-the-art methods.

Indirect methods for fuel-minimal rendezvous with a large population of temporarily captured orbiters
Monique Chyba and Geoff Patterson
2019, 9(2) : 225-256 doi: 10.3934/naco.2019016 +[Abstract](127) +[HTML](69) +[PDF](1616.0KB)
Abstract:

A main objective of this work is to assess the feasibility of space missions to a new population of near Earth asteroids which temporarily orbit Earth, called temporarily captured orbiter. We design rendezvous missions to a large random sample from a database of over 16,000 simulated temporarily captured orbiters using an indirect method based on the maximum principle. The main contribution of this paper is the development of techniques to overcome the difficulty in initializing the algorithm with the construction of the so-called cloud of extremals.

Recent advances in numerical methods for nonlinear equations and nonlinear least squares
Ya-Xiang Yuan
2011, 1(1) : 15-34 doi: 10.3934/naco.2011.1.15 +[Abstract](1833) +[PDF](445.3KB) Cited By(27)
Control parameterization for optimal control problems with continuous inequality constraints: New convergence results
Ryan Loxton, Qun Lin, Volker Rehbock and Kok Lay Teo
2012, 2(3) : 571-599 doi: 10.3934/naco.2012.2.571 +[Abstract](1379) +[PDF](325.0KB) Cited By(18)
A modified Fletcher-Reeves-Type derivative-free method for symmetric nonlinear equations
Dong-Hui Li and Xiao-Lin Wang
2011, 1(1) : 71-82 doi: 10.3934/naco.2011.1.71 +[Abstract](1238) +[PDF](194.9KB) Cited By(16)
Univariate geometric Lipschitz global optimization algorithms
Dmitri E. Kvasov and Yaroslav D. Sergeyev
2012, 2(1) : 69-90 doi: 10.3934/naco.2012.2.69 +[Abstract](1265) +[PDF](602.3KB) Cited By(15)
Optimal control strategies for tuberculosis treatment: A case study in Angola
Cristiana J. Silva and Delfim F. M. Torres
2012, 2(3) : 601-617 doi: 10.3934/naco.2012.2.601 +[Abstract](1168) +[PDF](342.2KB) Cited By(13)
Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions
Walter Alt, Robert Baier, Matthias Gerdts and Frank Lempio
2012, 2(3) : 547-570 doi: 10.3934/naco.2012.2.547 +[Abstract](1242) +[PDF](298.8KB) Cited By(13)
Noether's symmetry Theorem for variational and optimal control problems with time delay
Gastão S. F. Frederico and Delfim F. M. Torres
2012, 2(3) : 619-630 doi: 10.3934/naco.2012.2.619 +[Abstract](1144) +[PDF](199.0KB) Cited By(12)
Towards globally optimal operation of water supply networks
Ambros M. Gleixner, Harald Held, Wei Huang and Stefan Vigerske
2012, 2(4) : 695-711 doi: 10.3934/naco.2012.2.695 +[Abstract](1524) +[PDF](810.5KB) Cited By(12)
An unconstrained optimization approach for finding real eigenvalues of even order symmetric tensors
Lixing Han
2013, 3(3) : 583-599 doi: 10.3934/naco.2013.3.583 +[Abstract](1251) +[PDF](442.5KB) Cited By(12)
Linearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming
Bingsheng He and Xiaoming Yuan
2013, 3(2) : 247-260 doi: 10.3934/naco.2013.3.247 +[Abstract](1387) +[PDF](461.8KB) Cited By(11)
A brief survey of methods for solving nonlinear least-squares problems
Hassan Mohammad, Mohammed Yusuf Waziri and Sandra Augusta Santos
2019, 9(1) : 1-13 doi: 10.3934/naco.2019001 +[Abstract](892) +[HTML](396) +[PDF](397.82KB) PDF Downloads(156)
Optimization problems with orthogonal matrix constraints
K. T. Arasu and Manil T. Mohan
2018, 8(4) : 413-440 doi: 10.3934/naco.2018026 +[Abstract](1218) +[HTML](221) +[PDF](716.28KB) PDF Downloads(143)
Linearly-growing reductions of Karp's 21 NP-complete problems
Jerzy A. Filar, Michael Haythorpe and Richard Taylor
2018, 8(1) : 1-16 doi: 10.3934/naco.2018001 +[Abstract](1382) +[HTML](367) +[PDF](300.52KB) PDF Downloads(111)
Performance evaluation of four-stage blood supply chain with feedback variables using NDEA cross-efficiency and entropy measures under IER uncertainty
Shiva Moslemi and Abolfazl Mirzazadeh
2017, 7(4) : 379-401 doi: 10.3934/naco.2017024 +[Abstract](1911) +[HTML](300) +[PDF](381.9KB) PDF Downloads(94)
Mathematical model of Chimeric Anti-gene Receptor (CAR) T cell therapy with presence of cytokine
Reihaneh Mostolizadeh, Zahra Afsharnezhad and Anna Marciniak-Czochra
2018, 8(1) : 63-80 doi: 10.3934/naco.2018004 +[Abstract](1801) +[HTML](539) +[PDF](271.19KB) PDF Downloads(87)
Solving optimal control problem using Hermite wavelet
Akram Kheirabadi, Asadollah Mahmoudzadeh Vaziri and Sohrab Effati
2019, 9(1) : 101-112 doi: 10.3934/naco.2019008 +[Abstract](574) +[HTML](289) +[PDF](359.78KB) PDF Downloads(81)
A projected preconditioned conjugate gradient method for the linear response eigenvalue problem
Xing Li, Chungen Shen and Lei-Hong Zhang
2018, 8(4) : 389-412 doi: 10.3934/naco.2018025 +[Abstract](720) +[HTML](170) +[PDF](474.37KB) PDF Downloads(74)
Positive and negative definite submatrices in an Hermitian least rank solution of the matrix equation AXA*=B
Sihem Guerarra
2019, 9(1) : 15-22 doi: 10.3934/naco.2019002 +[Abstract](520) +[HTML](297) +[PDF](327.08KB) PDF Downloads(74)
Fuzzy target-environment networks and fuzzy-regression approaches
Erik Kropat and Gerhard Wilhelm Weber
2018, 8(2) : 135-155 doi: 10.3934/naco.2018008 +[Abstract](977) +[HTML](142) +[PDF](310.66KB) PDF Downloads(68)
On a two-phase approximate greatest descent method for nonlinear optimization with equality constraints
M. S. Lee, B. S. Goh, H. G. Harno and K. H. Lim
2018, 8(3) : 315-326 doi: 10.3934/naco.2018020 +[Abstract](824) +[HTML](133) +[PDF](770.98KB) PDF Downloads(65)

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