Essential Solutions and Essential Components of the Solution Set of Infinite Dimensional Vector Optimization Problems
Dingtao Peng · Mathematica Applicata · 2009
The notes of essential solution and essential components of solution set for vector optimization are introduced in order to research the stability of weak efficient solution of general vector optimization including the infinite dimensional problems.We proved that there exists a dense Gδ subset of the complete metric space consisting of the vector optimization problems satisfying some conditions,and each problem in the dense Gδ subset has stable solution set,which generalized the corresponding results in the literature.We discussed the essential component of solution set and proved that if the solution set can be decomposed two or more components,there is no essential component.As a result,we gave a sufficient and necessary condition for the existence of the essential component.