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arXiv · 2002.09368

Global Optimization via the Dual SONC Cone and Linear Programming

Mareike Dressler·Janin Heuer·Helen Naumann·Timo de Wolff
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Abstract

Using the dual cone of sums of nonnegative circuits (SONC), we provide a relaxation of the global optimization problem to minimize an exponential sum and, as a special case, a multivariate real polynomial. Our approach builds on two key observations. First, that the dual SONC cone is contained in the primal one. Hence, containment in this cone is a certificate of nonnegativity. Second, we show that membership in the dual cone can be verified by a linear program. We implement the algorithm and present initial experimental results comparing our method to existing approaches.

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Mareike Dressler, Janin Heuer, Helen Naumann, Timo de Wolff. 2020-02-21. Global Optimization via the Dual SONC Cone and Linear Programming. https://doi.org/10.1145/3373207.3404043

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