A Characterization for Tightness of the Sparse Moment-SOS Hierarchy
arxiv(2024)
Abstract
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.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined