Rentsen Enkhbat

Joint power control, base station assignment, and channel assignment in cognitive femtocell networks

Cognitive radio and femtocells are recent technology breakthroughs that aim to achieve throughput improvement by means of spectrum management and interference mitigation, respectively. However, these technologies are limited by the formers susceptibility to interference and the latters dependence on bandwidth availability. In this paper, we overcome these limitations by integrating cognitive radio and femtocell technology and exploring its feasibility and throughput improvement. To realize this, we propose an integrated architecture and formulate a multiobjective optimization problem with mixed integer variables for the joint power control, base station assignment, and channel assignment scheme. In order to find a pareto optimal solution, a weighted sum approach was used. Based on numerical results, the optimization framework is found to be both stable and converging. Simulation studies further show that the proposed architecture and optimization framework improve the aggregate throughput as the client population rises, hence confirming the successful and beneficial integration of these technologies.

Optimization and optimal control

Extragradient Approach to the Solution of Two Person Non-Zero Sum Games (A Antipin) Nonlinear Phenomena in Economics (S Budnyam) On Some Theory, Methods and Algorithms for Concave Programming (R Enkhbat) Maximum Clique Regularizations (D Fortin & I Tseveendorj) The Role of Optimization in Economics (D W Katzner) A Global Optimization Approach to Solving Equilibrium Programming Problems (O Khamisov) Comparison of Convex Relaxations for Monomials of Odd Degree (L Liberti) Structural Stability of Vector Optimization Problems (P Mbunga) Optimization for Black-Box Objective Functions (H Nakayama et al.) New Variants of Gradient Type Methods in Optimal Control Problems (V A Srochko) Controlled Systems with Distributed Parameters: Optimally Conditions and Optimization Methods in Class of Smooth Restricted Controls (O V Vasiliev) The Points of a Linear Manifold Nearest to a Given Vector (V I Zorkaltsev) and other articles.

Conditional gradient Tikhonov method for a convex optimization problem in image restoration

In this paper, we consider the problem of image restoration with Tikhonov regularization as a convex constrained minimization problem. Using a Kronecker decomposition of the blurring matrix and the Tikhonov regularization matrix, we reduce the size of the image restoration problem. Therefore, we apply the conditional gradient method combined with the Tikhonov regularization technique and derive a new method. We demonstrate the convergence of this method and perform some numerical examples to illustrate the effectiveness of the proposed method as compared to other existing methods.

Optimization, Simulation, and Control

Optimization, simulation and control play an increasingly important role in science and industry. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace.This volume brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. The book is composed of invited contributions by experts from around the world who work to develop and apply new optimization, simulation and control techniques either at a theoretical level or in practice. Some key topics presented include: equilibrium problems, multi-objective optimization, variational inequalities, stochastic processes, numerical analysis, optimization in signal processing, and various other interdisciplinary applications.This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization, simulation and control can be applied.

Global minimization algorithms for concave quadratic programming problems

Abstract: In this article, we consider the concave quadratic programming problem which is known to be NP hard. Based on the improved global optimality conditions by [Dür, M., Horst, R. and Locatelli, M., 1998, Necessary and sufficient global optimality conditions for convex maximization revisited, Journal of Mathematical Analysis and Applications, 217, 637–649] and [Hiriart-Urruty, J.B. and Ledyav, J.S., 1996, A note in the characterization of the global maxima of a convex function over a convex set, Journal of Convex Analysis, 3, 55–61], we develop a new approach for solving concave quadratic programming problems. The main idea of the algorithms is to generate a sequence of local minimizers either ending at a global optimal solution or at an approximate global optimal solution within a finite number of iterations. At each iteration of the algorithms we solve a number of linear programming problems with the same constraints of the original problem. We also present the convergence properties of the proposed algorithms under some conditions. The efficiency of the algorithms has been demonstrated with some numerical examples.

Polymatrix games and optimization problems

Consideration was given to the properties of the polymatrix game, a finite noncooperative game of N players (N ⩾ 3). A theorem of reduction of the search for Nash equilibria to an optimization problem was proved. This clears the way to the numerical search of equilibria. Additionally, a simple proof of the Nash theorem of existence of equilibrium in the polymatrix game was given using the theorem of existence of solution in the optimization problem.

A novel approach for nonconvex optimal control problems

The nonconvex optimal control problem with the concave terminal objective function has been considered. First, the problem reduces to the concave minimization problem and then we apply the global optimality condition given by Strekalovsky [On the global extremum problem, Soviet Math. Doklady 292 (1987), pp. 1062–1066.] to the problem. Based on the global optimality condition, we propose a method for improving a current stationary process in the problem. The proposed method has been tested on some example problems.

A Numerical Approach for Solving Some Convex Maximization Problems

We are concerned with concave programming or the convex maximization problem. In this paper, we propose a method and algorithm for solving the problem which are based on the global optimality conditions first obtained by Strekalovsky (Soviet Mathematical Doklady, 8(1987)). The method continues approaches given in (Journal of global optimization, 8(1996); Journal of Nolinear and convex Analyses 4(1)(2003)). Under certain assumptions a convergence property of the proposed method has been established. Some computational results are reported. Also, it has been shown that the problem of finding the largest eigenvalue can be found by the proposed method.

A global optimization approach for solving non-monotone variational inequality problems

The aim of this article is to reformulate the non-monotone variational inequality problem as a global optimization problem and present a branch and bound method for solving it. Under a mild condition, it is shown that the equivalent optimization problem enjoys a Lipschitz property. The proposed approach is illustrated with computational experiments.

A global method for some class of optimization and control problems

The problem of maximizing a nonsmooth convex function over an arbitrary set is considered. Based on the optimality condition obtained by Strekalovsky in 1987 an algorithm for solving the problem is proposed. We show that the algorithm can be applied to the nonconvex optimal control problem as well. We illustrate the method by describing some computational experiments performed on a few nonconvex optimal control problems.