广义凸向量优化的Benson真有效性  

Benson Proper Efficiency in Generalized Convex Vector Optimization

作　　者：贾继红[1] 孙大巍[1] 

机构地区：[1]东莞理工学院计算机学院,广东东莞523808

出　　处：《东莞理工学院学报》2010年第1期5-8,共4页Journal of Dongguan University of Technology

摘　　要：在拟锥次类凸假设下,研究了局部凸Hausdorff拓扑向量空间中拟锥次类凸映射的向量优化问题。建立了向量优化的Benson真有效解和相应的标量化问题的最优解之间的关系,以及和相应的无约束向量极小化问题的Benson真有效解之间的关系。结果表明:第一,在一定条件下,向量优化的Benson真有效解与其相应的标量化问题的最优解等价;第二,在一定条件下,向量优化的Benson真有效解是其相应的无约束向量极小化问题的Benson真有效解。This paper studies nearly cone-subconvexlike vector optimization in locally-convex Hausdorff topological vector spaces by alternative theorem of nearly eone-subconvexlike maps. It points out the relations between Benson proper efficiency in vector optimization and optimal solution in scalarization problems and establishes Benson proper efficiency in unconstraint vector optimization under nearly cone-subconvexlikeness. The results indicate that under some conditions Benson proper efficiency in vector optimization is the same as the optimal solution in scalarization problems, and as Benson proper efficiency in unconstraint vector optimization.

关 键 词：最优化 择一定理 拟锥次似凸 BENSON真有效解 

分 类 号：O224[理学—运筹学与控制论]