An Efficient Framework for Global Non-Convex Polynomial Optimization with Algebraic Constraints
Optimization and Control
2024-09-05 v2 Mathematical Software
Numerical Analysis
Numerical Analysis
Abstract
We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that possesses essentially no spurious local minima. Through numerical experiments on previously intractable global constrained polynomial optimization problems in high dimension, we show that polynomial scaling in dimension and degree is achievable when computing the optimal value and location.
Cite
@article{arxiv.2311.02037,
title = {An Efficient Framework for Global Non-Convex Polynomial Optimization with Algebraic Constraints},
author = {Mitchell Tong Harris and Pierre-David Letourneau and Dalton Jones and M. Harper Langston},
journal= {arXiv preprint arXiv:2311.02037},
year = {2024}
}