多目标半定规划的互补弱鞍点和G-鞍点最优性条件

摘要

Multiobjective semidefinite programming with a semidefinite constraint is studied in this paper. The definitions and equivalent definitions of the weak saddle point under the means of the weak efficient solution and the G-saddle point under the means of the G-efficient solution are given. The saddle point type necessary and sufficient conditions are obtained by an alternative theorem under a weakly convex condition.%对于含矩阵函数半定约束和多个目标函数的多目标半定规划问题,给出La-grange函数在弱有效意义下的互补弱鞍点和Geoffrion恰当有效意义下的G-鞍点的定义及其等价定义.然后,在较弱的凸性条件下,利用含矩阵和向量约束的择一性定理,建立多目标半定规划的互补弱鞍点和G-鞍点充分必要条件.