An Efficient Framework for Global Non-Convex Polynomial Optimization with Algebraic Constraints
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912013859422208 |
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| author | Harris, Mitchell Tong Letourneau, Pierre-David Jones, Dalton Langston, M. Harper |
| author_facet | Harris, Mitchell Tong Letourneau, Pierre-David Jones, Dalton Langston, M. Harper |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02037 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Efficient Framework for Global Non-Convex Polynomial Optimization with Algebraic Constraints Harris, Mitchell Tong Letourneau, Pierre-David Jones, Dalton Langston, M. Harper Optimization and Control Mathematical Software Numerical Analysis 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. |
| title | An Efficient Framework for Global Non-Convex Polynomial Optimization with Algebraic Constraints |
| topic | Optimization and Control Mathematical Software Numerical Analysis |
| url | https://arxiv.org/abs/2311.02037 |