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 Global Optimization Algorithm for Signomial Geometric Programming Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Xue-Ping Hou ◽  
Pei-Ping Shen ◽  
Yong-Qiang Chen
Keyword(s):  
Linear Programming ◽  
Global Optimization ◽  
Programming Problem ◽  
Optimization Algorithm ◽  
Geometric Programming ◽  
Nonconvex Programming ◽  
Algebraic Manipulation ◽  
Global Optimization Algorithm ◽  
Linear Programming Problems ◽  
Signomial Geometric Programming

This paper presents a global optimization algorithm for solving the signomial geometric programming (SGP) problem. In the algorithm, by the straight forward algebraic manipulation of terms and by utilizing a transformation of variables, the initial nonconvex programming problem (SGP) is first converted into an equivalent monotonic optimization problem and then is reduced to a sequence of linear programming problems, based on the linearizing technique. To improve the computational efficiency of the algorithm, two range reduction operations are combined in the branch and bound procedure. The proposed algorithm is convergent to the global minimum of the (SGP) by means of the subsequent solutions of a series of relaxation linear programming problems. And finally, the numerical results are reported to vindicate the feasibility and effectiveness of the proposed method.

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.

A Global Optimization Algorithm for Solving Linear Programming Problem

1997 ◽  
Vol 30 (19) ◽  
pp. 513-515
Author(s):  
José Ranieri Ribeiro Cavalcante ◽  
Fernando Menezes Campello de Souza
Keyword(s):  
Linear Programming ◽  
Global Optimization ◽  
Programming Problem ◽  
Optimization Algorithm ◽  
Linear Programming Problem ◽  
Global Optimization Algorithm

scholarly journals Linear-quadratic programming and its application to data correction of improper linear programming problems

2020 ◽  
Vol 10 (1) ◽  
pp. 48-55
Author(s):  
Victor Gorelik ◽  
Tatiana Zolotova
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Linear Programming Problem ◽  
Optimization Problems ◽  
Lagrange Function ◽  
Frobenius Norm ◽  
Linear Quadratic ◽  
Quadratic Constraints ◽  
Linear Programming Problems ◽  
The Right

AbstractThe problem of maximizing a linear function with linear and quadratic constraints is considered. The solution of the problem is obtained in a constructive form using the Lagrange function and the optimality conditions. Many optimization problems can be reduced to the problem of this type. In this paper, as an application, we consider an improper linear programming problem formalized in the form of maximization of the initial linear criterion with a restriction to the Euclidean norm of the correction vector of the right-hand side of the constraints or the Frobenius norm of the correction matrix of both sides of the constraints.

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