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SONC Optimization and Exact Nonnegativity Certificates via Second-Order Cone Programming

Abstract : The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice to investigate which convex cones admit a representation using SOCs, given that they have a strong expressive ability. In this paper, we prove constructively that the cone of sums of nonnegative circuits (SONC) admits an SOC representation. Based on this, we give a new algorithm for unconstrained polynomial optimization via SOC programming. We also provide a hybrid numeric-symbolic scheme which combines the numerical procedure with a rounding-projection algorithm to obtain exact nonnegativity certificates. Numerical experiments demonstrate the efficiency of our algorithm for polynomials with fairly large degree and number of variables.
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https://hal.laas.fr/hal-03070864
Contributor : Victor Magron Connect in order to contact the contributor
Submitted on : Wednesday, December 16, 2020 - 8:31:02 AM
Last modification on : Wednesday, August 31, 2022 - 4:43:23 PM

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Victor Magron, Jie Wang. SONC Optimization and Exact Nonnegativity Certificates via Second-Order Cone Programming. Journal of Symbolic Computation, Elsevier, 2023, 115, pp.346-370. ⟨10.1016/j.jsc.2022.08.002⟩. ⟨hal-03070864⟩

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