An approach to constrained polynomial optimization via nonnegative circuit polynomials and geometric programming. (March 2019)

• Record Type: Journal Article
• Authors: Dressler, Mareike; Iliman, Sadik; de Wolff, Timo
• Is Part Of: Journal of symbolic computation. Volume 91(2019)
• Page Start: 149
• Page End: 172
• Publication Date: 2019-03
• Subjects: 12D15 -- 14P99 -- 52B20 -- 90C25; Certificate -- Geometric programming -- Nonnegative polynomial -- Semidefinite programming -- Sum of nonnegative circuit polynomials -- Sum of squares -- Triangulation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.06.018
• Languages: English
• ISSNs: 0747-7171

Abstract

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.