A unified concept of approximate and quasi efficient solutions and associated subdifferentials in multiobjective optimization

• 成果类型: Article
• 署名作者: Huerga, L.; Jimenez, B.; Luc, D. T.; Novo, V.
• 署名单位: Universidad Nacional de Educacion a Distancia (UNED); Ton Duc Thang University; Ton Duc Thang University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01597-9
• 发表日期: 2021
• 页码: 379-407
• 关键词: vector optimization; optimality conditions; epsilon-subdifferentials; variational principle; proper efficiency; sets

摘要

In this paper, we introduce some new notions of quasi efficiency and quasi proper efficiency for multiobjective optimization problems that reduce to the most important concepts of approximate and quasi efficient solutions given up to now. We establish main properties and provide characterizations for these solutions by linear and nonlinear scalarizations. With the help of quasi efficient solutions, a generalized subdifferential of a vector mapping is introduced, which generates a number of approximate subdifferentials frequently used in optimization in a unifying way. The generalized subdifferential is related to the classical subdifferential of real functions by the method of scalarization. An application of generalized subdifferential to express optimality conditions for quasi efficient solutions is also given.