一类非凸多目标规划问题的组合同伦内点法  

Combined homotopy interior-point method for a class of nonconvex multi-objective programming problem

作　　者：贺莉[1] 金鉴禄[1] 赵嘉琦[1] 刘庆怀[1] 

机构地区：[1]长春工业大学基础科学学院,长春130012

出　　处：《黑龙江大学自然科学学报》2010年第5期693-697,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10771020);吉林省自然科学基金资助项目(20101599)

摘　　要：对一类非凸域上的多目标规划问题通过减弱非凸可行域的边界条件,在其满足伪锥条件下,利用组合同伦内点法证明几乎对可行域的任一内点,均产生一条光滑、有界的同伦路径,并证明了该方法是整体收敛于多目标优化问题的K-K-T点,从而扩大了组合同伦内点法的应用范围,为求解非凸多目标优化问题的最小弱有效解或其他意义下的最优解提供了一种新的方法。By weakening the boundary condition of nonconvex feasible region,a combined homotopy interior method for a class of nonconvex multi-objective programming problem with pseudo cone condition is suggested.It is shown that for almost every interior point in the feasible region,a smooth and bounded homotopy path could be derived with pseudo cone condition.It is also proved that the algorithm converges to the K-K-T point of multi-objective programming problem.The results expanded the application of combined homotopy interior method,and provided a new way for finding the minimal weak efficient solutions and other optimistic solutions of nonconvex multi-objective programming problem.

关 键 词：非凸多目标规划 伪锥条件 同伦内点法 

分 类 号：O221.6[理学—运筹学与控制论]