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AN APPROACH TO CONSTRAINED POLYNOMIAL OPTIMIZATION VIA NONNEGATIVE CIRCUIT POLYNOMIALS AND GEOMETRIC PROGRAMMING

Abstract : In this article we combine two developments in polynomial optimization. On the one hand, we consider nonnegativity certificates based on sums of nonnegative circuit polynomials, which were recently introduced by the second and the third author. On the other hand, we investigate geometric programming methods for constrained polynomial optimization problems, which were recently developed by Ghasemi and Marshall. We show that the combination of both results yields a new method to solve certain classes of constrained polynomial optimization problems. We test the new method experimentally and compare it to semidefinite programming in various examples.
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https://hal.inria.fr/hal-01829714
Contributor : Alain Monteil <>
Submitted on : Wednesday, July 4, 2018 - 11:48:09 AM
Last modification on : Monday, December 28, 2020 - 10:22:04 AM
Long-term archiving on: : Monday, October 1, 2018 - 2:01:36 PM

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Mareike Dressler, Sadik Iliman, Timo de Wolff. AN APPROACH TO CONSTRAINED POLYNOMIAL OPTIMIZATION VIA NONNEGATIVE CIRCUIT POLYNOMIALS AND GEOMETRIC PROGRAMMING. MEGA 2017 - International Conference on Effective Methods in Algebraic Geometry, Jun 2017, Nice, France. ⟨hal-01829714⟩

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