Work

A characterization for tightness of the sparse Moment-SOS hierarchy

Year: 2025

Type: article

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.

Source: Mathematical Programming

DOI: 10.1007/s10107-025-02223-2

Authors: Jiawang Nie, Zheng Qu, Xindong Tang, Linghao Zhang

Institutions: University of California San Diego, Hong Kong Polytechnic University, Hong Kong Baptist University

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: National Science Foundation, American Institute of Mathematics, Hong Kong Baptist University