Optimality conditions for homogeneous polynomial optimization on the unit sphere

Lei Huang

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arXiv · 2111.01971

Optimality conditions for homogeneous polynomial optimization on the unit sphere

Lei Huang

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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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Lei Huang. 2021-11-03. Optimality conditions for homogeneous polynomial optimization on the unit sphere. https://arxiv.org/abs/2111.01971

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