Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization

• 成果类型: Article
• 署名作者: Crespi, Giovanni Paolo; Hamel, Andreas H.; Rocca, Matteo; Schrage, Carola
• 署名单位: Universita Carlo Cattaneo - Liuc; Free University of Bozen-Bolzano; University of Insubria
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1060
• 发表日期: 2021
• 页码: 361-381
• 关键词: well-posedness; optimality conditions; vector optimization; scalarization; convexity; Duality

摘要

Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponding complete lattice of sets. Functions mapping into the preordered set are extended to complete lattice-valued ones, and concepts for exact and approximate solutions for corresponding set optimization problems are introduced and existence results are given. Well-posedness for complete lattice-valued problems is introduced and characterized. The new approach is compared with existing ones in vector and set optimization. Its relevance is shown by means of many examples from multicriteria decision making, statistics, and mathematical economics and finance.