Necessary Nondomination Conditions in Set and Vector Optimization with Variable Ordering Structures
In this paper we study the concept of nondomination in problems of set and vector optimization with variable ordering structures, which reduces to Pareto efficiency when the ordering structure is constant/nonvariable. Based on advanced tools of variational analysis and generalized differentiation, we develop verifiable necessary conditions for nondominated points of sets and for nondominated solutions to vector optimization problems with general geometric constraints that are new in both finite and infinite dimensions. Many examples are provided to illustrate and highlight the major features of the obtained results.
set and vector optimization variable ordering structures generalized differentiation nondominated solutions set-valued and variational analysis banach and asplund spaces