Representation of positive polynomials on a generalized strip and its application to polynomial optimization

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-11 DOI:10.1007/s11590-023-02087-5

引用次数: 0

Abstract

We study the representation of nonnegative polynomials in two variables on a certain class of unbounded closed basic semi-algebraic sets (which are called generalized strips). This class includes the strip \([a,b] \times {\mathbb {R}}\) which was studied by Marshall in (Proc Am Math Soc 138(5):1559–1567, 2010). A denominator-free Nichtnegativstellensätz holds true on a generalized strip when the width of the generalized strip is constant and fails otherwise. As a consequence, we confirm that the standard hierarchy of semidefinite programming relaxations defined for the compact case can indeed be adapted to the generalized strip with constant width. For polynomial optimization problems on the generalized strip with non-constant width, we follow Ha-Pham’s work: Solving polynomial optimization problems via the truncated tangency variety and sums of squares.

查看原文本刊更多论文

正多项式在广义条带上的表示及其在多项式优化中的应用

摘要我们研究了两变量非负多项式在某类无界封闭基本半代数集合（称为广义条带）上的表示。这一类包括 Marshall 在 (Proc Am Math Soc 138(5):1559-1567, 2010) 中研究过的条（[a,b] \times {\mathbb {R}}）。当广义条带的宽度恒定时，广义条带上的无分母 Nichtnegativstellensätz 成立，反之则不成立。因此，我们证实了在紧凑情况下定义的半定式编程松弛的标准层次确实可以适用于宽度恒定的广义条带。对于宽度非恒定的广义条带上的多项式优化问题，我们遵循 Ha-Pham 的工作方法：通过截切线和平方和解决多项式优化问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.