求解一般凸多目标规划最小弱有效解的组合同伦内点方法  

Combined Homotopy Interior Point Method of SolvingMinimal Weak Efficient Solution for General ConvexMulti-objective Programming

作　　者：安玉伟[1] 刘庆怀[2] 

机构地区：[1]黑龙江科技学院基础部,黑龙江鸡西158105 [2]吉林大学数学系,吉林长春130025

出　　处：《黑龙江科技学院学报》2002年第2期31-34,共4页Journal of Heilongjiang Institute of Science and Technology

基　　金：国家自然科学基金资助项目(19771043)

摘　　要：构造求解一般凸多目标规划等价的单目标规划K-K-T点的同伦方程,在M-F约束规定及外法锥条件下,证明了几乎对多目标规划可行域的任一内点,同伦方程可产生一条光滑、有界的同伦路径,并证明了数值追踪同伦路径将得到一般凸多目标规划最小弱有效解。In this paper, a homotopy equation has been constructed for getting the K-K-T point of the single objective programming, which is equivalent to the general convex multi-objective programming. As proved in the paper, a smooth and bounded homotopy path can be generated by the homotopy equation for almost every interior point of the feasible region of multi-objective programming, and numerical trace homotopy path can lead to a minimal weak efficient solution for convex multi-objective programming, under M-F constricted qualification and normal cone condition.

关 键 词：多目标规划 同伦方法 内点法 M-F约束 外法锥 

分 类 号：O221[理学—运筹学与控制论]