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

Mitchell Tong Harris; Pierre-David Letourneau; Dalton Jones; M. Harper Langston

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arXiv · 2311.02037

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

Mitchell Tong Harris·Pierre-David Letourneau·Dalton Jones·M. Harper Langston

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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.

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Mitchell Tong Harris, Pierre-David Letourneau, Dalton Jones, M. Harper Langston. 2023-11-03. An Efficient Framework for Global Non-Convex Polynomial Optimization with Algebraic Constraints. https://arxiv.org/abs/2311.02037

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