广义凸向量优化的Benson真有效性

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。

Benson Proper Efficiency in Generalized Convex Vector Optimization

This paper studies nearly cone-subconvexlike vector optimization in locally-convex Hausdorff topological vector spaces by alternative theorem of nearly cone-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 optimizat...