English

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 ff 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 ff is generic.

Keywords

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}
}
R2 v1 2026-06-24T07:23:41.874Z