A Characterization for Tightness of the Sparse Moment-SOS Hierarchy

Autor:	Nie, Jiawang, Qu, Zheng, Tang, Xindong, Zhang, Linghao
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if the objective can be written as a sum of sparse nonnegative polynomials, each of which belongs to the sum of the ideal and quadratic module generated by the corresponding sparse constraints. Based on this characterization, we give several sufficient conditions for the sparse Moment-SOS hierarchy to be tight. In particular, we show that this sparse hierarchy is tight under some assumptions such as convexity, optimality conditions or finiteness of constraining sets. Comment: 27 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.06882 Zobrazit plný text záznamu View this record from Arxiv