Polynomial Optimization Over Unions of Sets

Jiawang Nie; Linghao Zhang

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arXiv · 2404.17717

Polynomial Optimization Over Unions of Sets

Jiawang Nie·Linghao Zhang

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Abstract

This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove the asymptotic or finite convergence of the unified hierarchy. Special properties for the univariate case are discussed.The application for computing $(p,q)$-norms of matrices is also presented.

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BibTeX RIS

Jiawang Nie, Linghao Zhang. 2024-04-26. Polynomial Optimization Over Unions of Sets. https://arxiv.org/abs/2404.17717

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