An Efficient Framework for Global Non-Convex Polynomial Optimization with Algebraic Constraints

An Efficient Framework for Global Non-Convex Polynomial Optimization with Algebraic Constraints

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 nume...

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Veröffentlicht in:arXiv.org 2024-09
Hauptverfasser: Mitchell Tong Harris, Pierre-David Letourneau, Jones, Dalton, M Harper Langston
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Constraints
Optimization
Polynomials
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Pierre-David Letourneau
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M Harper Langston
description 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.
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Polynomials
title An Efficient Framework for Global Non-Convex Polynomial Optimization with Algebraic Constraints
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