Optimality conditions for homogeneous polynomial optimization on the unit sphere

2021/11/03 by Huang, Lei · 3 citations
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2111.01971

Abstract

In this note, we prove that for homogeneous polynomial optimization on the sphere, if the objective f is generic in the input space, all feasible points satisfying the first order and second order necessary optimality conditions are local minimizers, which addresses an issue raised in the recent work by Lasserre (Optimization Letters, 2021). As a corollary, this implies that Lasserre's hierarchy has finite convergence when f is generic.

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• Finite Convergence of the Moment-SOS Hierarchy on the Product of Spheres
• Lagrange multiplier expressions for matrix polynomial optimization and tight relaxations
• Convergence rates for polynomial optimization on set products

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• Optimality Conditions and Finite Convergence of Lasserre's Hierarchy
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