Theory and applications of the Sum-Of-Squares technique

Francis Bach; Elisabetta Cornacchia; Luca Pesce; Giovanni Piccioli

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arXiv · 2306.16255

Theory and applications of the Sum-Of-Squares technique

Francis Bach·Elisabetta Cornacchia·Luca Pesce·Giovanni Piccioli

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Abstract

The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space, the SOS method transforms non-convex global optimization problems into solvable semidefinite programs. This note presents an overview of the SOS method. We start with its application in finite-dimensional feature spaces and, subsequently, we extend it to infinite-dimensional feature spaces using reproducing kernels (k-SOS). Additionally, we highlight the utilization of SOS for estimating some relevant quantities in information theory, including the log-partition function.

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Francis Bach, Elisabetta Cornacchia, Luca Pesce, Giovanni Piccioli. 2023-06-28. Theory and applications of the Sum-Of-Squares technique. https://arxiv.org/abs/2306.16255

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