带多乘积约束的非凸二次规划的全局优化  

GLOBAL OPTIMIZATION FOR NON-CONVEX QUADRATIC PROGRAMS WITH ADDITIONAL MULTIPLICATIVE CONSTRAINTS

作　　者：申培萍[1] 王俊华[1] 汤廉洁 

机构地区：[1]河南师范大学数学与信息科学学院,新乡453007

出　　处：《高等学校计算数学学报》2013年第4期295-301,共7页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11171094;10671057)

摘　　要：1引言考虑如下带多乘积约束的二次规划问题:■其中,c∈Rn,Q∈Rn×n为对称阵,A∈Rq×n,d∈Rq,S0是单纯形,Ψkj（x）是仿射函数且在S0上Ψkj（x）】0.问题（P）能广泛应用于微观经济学、超大规模集成电路芯片设计、债券投资组合优化等领域[1,2].因问题（P）存在多个非全局最优的局部解,使得对其求解极其困难.This paper presents a branch and duality bound algorithm for glob- ally solving a class of non-convex quadratic programming problems with additional multiplicative constraints. The algorithm uses Lagrange duality theory to convert the bounding subproblems during the algorithm into a sequence of linear program- ming problems, which can be solved very efficiently. The numerical results show that the proposed algorithm is effective.

关 键 词：带多乘积约束 非凸二次规划 全局优化 高等数学 

分 类 号：O221.2[理学—运筹学与控制论]