ISSN:

2155-3289

eISSN:

2155-3297

## Numerical Algebra, Control & Optimization

September 2020 , Volume 10 , Issue 3

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**Abstract:**

We introduce and suggest to research a special class of optimization problems, wherein an objective function is a real-valued complex variables function under constraints, comprising complex-valued complex variables functions: "Complex Optimization". We demonstrate multiple examples to show a rich variety of problems, describing Complex Optimization as an optimization subclass as well as a Mixed Integer-Real-Complex Optimization.

Next, we introduce more general concept: "Quaternionic Optimization" for optimization over quaternion subsets.

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**Abstract:**

Allocation problem is an important issue in management. Data envelopment analysis (DEA) is a non-parametric method for assessing a set of decision making units (DMUs). It has proven to be a useful technique to solve allocation problems. In recent years, many papers have been published in this regard and many researchers have tried to find a suitable allocation model based on DEA. Common set of weights (CSWs) is a DEA model which, in contrast with traditional DEA models, does not allow individual weights for each decision making unit. In this manner, all DMUs are assessed through choosing a same set of weights. In this article, we will use the weighted-sum method to solve the multi-objective CSW problem. Then, via introducing a set of special weights, we will connect the CSW model to a non-linear (fractional) CSW model. After linearization, the proposed model is used for allocating resources. To illustrate our model, some examples are also provided.

*+*[Abstract](981)

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**Abstract:**

This work is deals with the numerical solution of a bilateral obstacle optimal control problem which is similar to the one given in Bergounioux et al [

*+*[Abstract](985)

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**Abstract:**

In this paper, we study the problem of minimizing the ratio of two quadratic functions subject to two quadratic constraints in the complex space. Using the classical Dinkelbach method, we transform the problem into a parametric nonlinear equation. We show that an optimal parameter can be found by employing the S-procedure and semidefinite relaxation technique. A key element to solve the original problem is to use the rank-one decomposition procedure. Finally, within the new algorithm, semidefinite relaxation is compared with the bisection method for finding the root on several examples. For further comparison, the solution of fmincon command of MATLAB also is reported.

*+*[Abstract](1031)

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**Abstract:**

In many global optimization techniques, the local search methods are used for different issues such as to obtain a new initial point and to find the local solution rapidly. Most of these local search methods base on the smoothness of the problem. In this study, we propose a new smoothing approach in order to smooth out non-smooth and non-Lipschitz functions playing a very important role in global optimization problems. We illustrate our smoothing approach on well-known test problems in the literature. The numerical results show the efficiency of our method.

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**Abstract:**

This paper studies the

*+*[Abstract](971)

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**Abstract:**

In this paper, the problem of sliding mode control (SMC) for uncertain T-S (Tagaki-Sugeno) fuzzy systems with input and state delays is investigated, in which the nonlinear uncertain terms are unknown, and also unmatched. For the T-S fuzzy model of the controlled object, a method based on sliding mode compensator is designed, and the system is controlled by sliding mode. Based on solving linear matrix inequalities (LMI), we obtain the design method of sliding mode and controller. The sufficient conditions for the asymptotical stability of the sliding mode dynamics are given by using LMI technique and the Lyapunov stability theory, and it has been shown that the state trajectories can be driven onto the sliding surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theories.

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**Abstract:**

Fuzzy time series shows great advantages in dealing with incomplete or unreasonable data. But most of them are based on fuzzy AR time series model, so it is necessary to add MA variables to the fuzzy time series [

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**Abstract:**

This paper presents a observer-based fault estimation method for a class of singularly perturbed systems subjected to parameter uncertainties and time-delay in state and disturbance signal with finite energy. To solve the estimation problem involving actuator fault and sensor fault for the uncertain disturbed singularly perturbed systems with time-delay, the problem we studied is firstly transformed into a standard

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**Abstract:**

This paper studies the problem of passive control for a class of uncertain nonlinear lower-triangle systems. We extend the feedback designing tool named adding a power integrator. By using it repeatedly, the passive controller is given. Under this designing method, we don't need the system to be feedback linearizable. Moreover, comparing with the backstepping technique, the coordinate in the controller designing process of this method does not need to be transformed.

*+*[Abstract](832)

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**Abstract:**

A differential algebraic nutrient-plankton-fish model with taxation, free fishing zone, protected zone and multiple delays is investigated in this paper. First, the conditions of existence and control of singularity induced bifurcation are given by regarding economic interest as bifurcation parameter. Meanwhile, the existence of Hopf bifurcations are investigated when migration rates, taxation and the cost per unit harvest are taken as bifurcation parameters respectively. Next, the local stability of the interior equilibrium, existence and properties of Hopf bifurcation are discussed in the different cases of five delays. Furthermore, the optimal tax policy is obtained by using Pontryagin's maximum principle. Finally, some numerical simulations are presented to demonstrate analytical results.

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