Necessary Nondomination Conditions in Set and Vector Optimization with Variable Ordering Structures

作者：Bao Truong Q^*; Mordukhovich Boris S

来源：Journal of Optimization Theory and Applications, 2014, 162(2): 350-370.

DOI：10.1007/s10957-013-0332-6

• Set-valued and variational analysis
• Set and vector optimization
• Variable ordering structures
• Nondominated solutions
• Generalized differentiation
• Banach and Asplund spaces

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.

• 出版日期2014-8