Multi-Degrees in Polynomial Optimization
Optimization and Control
2022-09-23 v1 Algebraic Geometry
Abstract
We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in several variables. For fixed multi-degrees we determine the generic number of complex critical points. This serves as a measure for the algebraic complexity of the optimization problem. We also discuss computation and certification methods coming from numerical nonlinear algebra.
Cite
@article{arxiv.2209.10670,
title = {Multi-Degrees in Polynomial Optimization},
author = {Kemal Rose},
journal= {arXiv preprint arXiv:2209.10670},
year = {2022}
}