Tangencies and polynomial optimization

• 成果类型: Article
• 署名作者: Tien-Son Pham
• 署名单位: Dalat University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01869-6
• 发表日期: 2023
• 页码: 1239-1272
• 关键词: gradient; INFINITY; squares; sums; sets

摘要

Given a polynomial function f : R-n -> R and an unbounded closed semi-algebraic set S subset of R-n, we show that the conditions listed below are characterized exactly in terms of the so-called tangency variety of the restriction of f on S: f is bounded from below on S; f attains its infimum on S; The sublevel sets (x is an element of S vertical bar f (x) <= lambda} for lambda is an element of R are compact; f is coercive on S. Besides, we also provide some stability criteria for boundedness and coercivity of f on S.