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边界约束非凸二次规划问题的分枝定界方法
引用本文:高岳林,徐成贤.边界约束非凸二次规划问题的分枝定界方法[J].运筹学学报,2001,5(4):81-89.
作者姓名:高岳林  徐成贤
作者单位:上西安交通大学理学院,
摘    要:本文是研究带有边界约束非凸二次规划问题,我们把球约束二次规划问题和线性约束凸二次规划问题作为子问题,分明引用了它们的一个求整体最优解的有效算法,我们提出几种定界的紧、松驰策略,给出了求解原问题整体最优解的分枝定界算法,并证明了该算法的收敛性,不同的定界组合就可以产生不同的分枝定界算法,最后我们简单讨论了一般有界凸域上非凸二次规划问题求整体最优解的分枝与定界思想。

关 键 词:非凸二次规划  分枝定界方法  整体优化  球约束  边界约束
修稿时间:2000年12月12

A Branch and Bound Method of the Nonconvex Quaclratic Programming Problem with Box Constraints
YUELIN GAO CHENGXIAN XU.A Branch and Bound Method of the Nonconvex Quaclratic Programming Problem with Box Constraints[J].OR Transactions,2001,5(4):81-89.
Authors:YUELIN GAO CHENGXIAN XU
Abstract:This paper researches the nonconvex quadratic programming problem with box constratints. We regard the ball constrained nonconvex quadratic programming problems and the linear constrained convex quadratic programming problems as subproblems. We make use of their efficient algorithms of the global optimization. We put forward several kinds of tight or slack bound schemes, and give the branch and bound algorithms of the global optimization of the former problem, as well as prove the cenrergent property of this algorithm, We can produce different branch and bound algorithms with different bound combinations. At last, We simply discuss the branch and bounded idea about the global optimization of the nonconvex quadratic programming problem on bounded convex field.
Keywords:nonconvex quadratic program  branch and bound method  global optimization  ball constraints  box constraints  
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