scholarly journals Global Optimization for Sum of Linear Ratios Problem Using New Pruning Technique

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Hongwei Jiao ◽  
Qigao Feng ◽  
Peiping Shen ◽  
Yunrui Guo
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Global Minimum ◽  
Linearization Method ◽  
Linear Constraints ◽  
Feasible Region ◽  
Global Optimization Algorithm ◽  
Equivalent Problem ◽  
Successive Refinement ◽  
Pruning Technique

A global optimization algorithm is proposed for solving sum of general linear ratios problem (P) using new pruning technique. Firstly, an equivalent problem (P1) of the (P) is derived by exploiting the characteristics of linear constraints. Then, by utilizing linearization method the relaxation linear programming (RLP) of the (P1) can be constructed and the proposed algorithm is convergent to the global minimum of the (P) through the successive refinement of the linear relaxation of feasible region and solutions of a series of (RLP). Then, a new pruning technique is proposed, this technique offers a possibility to cut away a large part of the current investigated feasible region by the optimization algorithm, which can be utilized as an accelerating device for global optimization of problem (P). Finally, the numerical experiments are given to illustrate the feasibility of the proposed algorithm.

scholarly journals Global Optimization for Solving Linear Multiplicative Programming Based on a New Linearization Method

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Chun-Feng Wang ◽  
Yan-Qin Bai
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Optimization Algorithm ◽  
Linearization Method ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Global Optimization Algorithm ◽  
Multiplicative Programming ◽  
Linear Multiplicative Programming ◽  
Pruning Techniques

This paper presents a new global optimization algorithm for solving a class of linear multiplicative programming (LMP) problem. First, a new linear relaxation technique is proposed. Then, to improve the convergence speed of our algorithm, two pruning techniques are presented. Finally, a branch and bound algorithm is developed for solving the LMP problem. The convergence of this algorithm is proved, and some experiments are reported to illustrate the feasibility and efficiency of this algorithm.

scholarly journals A Global Optimization Algorithm for Generalized Quadratic Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hongwei Jiao ◽  
Yongqiang Chen
Keyword(s):  
Linear Programming ◽  
Global Optimization ◽  
Quadratic Programming ◽  
Optimization Algorithm ◽  
Global Minimum ◽  
Nonconvex Programming ◽  
Nonconvex Quadratic Programming ◽  
Global Optimization Algorithm ◽  
Quadratic Constraints ◽  
Linear Programming Problems

We present a global optimization algorithm for solving generalized quadratic programming (GQP), that is, nonconvex quadratic programming with nonconvex quadratic constraints. By utilizing a new linearizing technique, the initial nonconvex programming problem (GQP) is reduced to a sequence of relaxation linear programming problems. To improve the computational efficiency of the algorithm, a range reduction technique is employed in the branch and bound procedure. The proposed algorithm is convergent to the global minimum of the (GQP) by means of the subsequent solutions of a series of relaxation linear programming problems. Finally, numerical results show the robustness and effectiveness of the proposed algorithm.

scholarly journals A New Global Optimization Algorithm for Solving Generalized Geometric Programming

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
San-Yang Liu ◽  
Chun-Feng Wang ◽  
Li-Xia Liu
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Geometric Programming ◽  
Optimal Solution ◽  
Global Optimization Algorithm ◽  
Global Optimal Solution ◽  
Linearization Technique ◽  
Generalized Geometric Programming ◽  
Global Optimal ◽  
Pruning Technique

A global optimization algorithm for solving generalized geometric programming (GGP) problem is developed based on a new linearization technique. Furthermore, in order to improve the convergence speed of this algorithm, a new pruning technique is proposed, which can be used to cut away a large part of the current investigated region in which the global optimal solution does not exist. Convergence of this algorithm is proved, and some experiments are reported to show the feasibility of the proposed algorithm.

Optimization Algorithm for Solving a Kind of Mathematical Problems

2010 ◽  
Vol 44-47 ◽  
pp. 3423-3426 ◽  
Author(s):  
Hong Wei Jiao ◽  
Kun Li
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Original Problem ◽  
Mathematical Problem ◽  
Relaxation Method ◽  
Linear Relaxation ◽  
Global Optimization Algorithm ◽  
Equivalent Problem ◽  
Numerical Examples ◽  
Mathematical Problems

In this paper, we develop an algorithm to globally solve a kind of mathematical problem. Firstly, by utilizing equivalent problem and linear relaxation method, a linear relaxation programming of original problem is established. Secondly, by using branch and bound technique, a determined global optimization algorithm is proposed for solving equivalent problem. Finally, the convergence of the proposed algorithm is proven and numerical examples showed that the presented algorithm is feasible to solve the kind of mathematical problems.

A global optimization algorithm for solving a four-person game

2017 ◽  
Vol 13 (3) ◽  
pp. 587-596
Author(s):  
S. Batbileg ◽  
N. Tungalag ◽  
A. Anikin ◽  
A. Gornov ◽  
E. Finkelstein
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Global Optimization Algorithm ◽  
Person Game
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