Optimality conditions for homogeneous polynomial optimization on the unit sphere
Optimization and Control
2022-10-05 v2
Abstract
In this note, we prove that for homogeneous polynomial optimization on the sphere, if the objective 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 is generic.
Cite
@article{arxiv.2111.01971,
title = {Optimality conditions for homogeneous polynomial optimization on the unit sphere},
author = {Lei Huang},
journal= {arXiv preprint arXiv:2111.01971},
year = {2022}
}