On the existence of Pareto solutions for polynomial vector optimization problems

• 成果类型: Article
• 署名作者: Kim, Do Sang; Tien-Son Pham; Nguyen Van Tuyen
• 署名单位: Pukyong National University; Hanoi Pedagogical University 2 (HPU2)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-018-1271-7
• 发表日期: 2019
• 页码: 321-341
• 关键词: sard theorem; set; images; VALUES

摘要

We are interested in the existence of Pareto solutions to the vector optimization problem where f:Rn -> Rm is a polynomial map. By using the tangency variety of f we first construct a semi-algebraic set of dimension at most m-1 containing the set of Pareto values of the problem. Then we establish connections between the Palais-Smale conditions, M-tameness, and properness for the map f. Based on these results, we provide some sufficient conditions for the existence of Pareto solutions of the problem. We also introduce a generic class of polynomial vector optimization problems having at least one Pareto solution.