Optimality Conditions at Infinity in Semialgebraic Vector Optimization

• 成果类型: Article; Early Access
• 署名作者: Jiao, Liguo; Lee, Jae Hyoung; Pham, Tien-Son
• 署名单位: Northeast Normal University - China; Pukyong National University; Dalat University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2024.0607
• 发表日期: 2025
• 关键词: Polynomials; minimizers; EXISTENCE; set

摘要

We are interested in optimality conditions for semialgebraic vector optimization problems with a situation in which generalized (weakly) nondominated points do exist but are not attained as image points of (weakly) efficient solutions. To this end, cones associated with unbounded semialgebraic sets at infinity are introduced and studied. Then, optimality conditions at infinity in terms of the Newton polyhedra of the objective mappings and of the cones associated with the constraint sets at infinity for the problems in question are proposed.