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Optimization Methods and Software
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An accelerated first-order method for solving SOS relaxations of unconstrained polynomial optimization problems

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Abstract

Our interest lies in solving sum of squares (SOS) relaxations of large-scale unconstrained polynomial optimization problems. Because interior-point methods for solving these problems are severely limited by the large-scale, we are motivated to explore efficient implementations of an accelerated first-order method to solve this class of problems. By exploiting special structural properties of this problem class, we greatly reduce the computational cost of the first-order method at each iteration. We report promising computational results as well as a curious observation about the behaviour of the first-order method for the SOS relaxations of the unconstrained polynomial optimization problem. © 2013 Copyright Taylor and Francis Group, LLC.

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Optimization Methods and Software

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