Uniform weak sharp minima for multiobjective optimization problems

Abstract

Noting that there exist abnormal phenomena in the existing weak sharp minima for multiobjective optimization problems, this paper introduces and studies uniform weak sharp minima for the multiobjective optimization problem. We first provide several characterizations for a piecewise linear multiobjective optimization problem with respect to the natural vector partial order induced by \BbbRn+ to have uniform weak sharp minima. Under a mild assumption, a piecewise linear multiobjective optimization problem with respect to an arbitrary vector partial order is proved to be equivalent to a piecewise linear multiobjective optimization problem with respect to the natural vector partial order. Based on such an interesting equivalence, this paper mainly establishes the uniform bounded and global weak sharp minima for a general piecewise linear multiobjective optimization problem with respect to any vector partial order.