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Sparse Copositive Polynomial Optimization

Year: 2026

Type: preprint

Abstract: This paper studies the copositive optimization problem whose objective is a sparse polynomial, with linear constraints over the nonnegative orthant. We propose sparse Moment-SOS relaxations to solve it. Necessary and sufficient conditions are shown for these relaxations to be tight. In particular, we prove they are tight under the cop-SOS convexity assumption. Compared to the traditional dense ones, the sparse Moment-SOS relaxations are more computationally efficient. Numerical experiments are given to show the efficiency.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2604.00180

Authors: Zhong, Suhan, Zhou, Jinling, Nie, Jiawang, Tang, Xindong

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

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Air Force Office of Scientific Research

Awards: G1523888516, Tight Relaxation Methods for Optimization

OpenAlex ID: W7148580107

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