An accelerated first-order method for solving SOS relaxations of unconstrained polynomial optimization problems
Author(s)Bertsimas, Dimitris J.; Freund, Robert Michael; Sun, Xu Andy
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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.
DepartmentSloan School of Management
Optimization Methods and Software
Taylor & Francis
Bertsimas, Dimitris, Robert M. Freund, and Xu Andy Sun. “An Accelerated First-Order Method for Solving SOS Relaxations of Unconstrained Polynomial Optimization Problems.” Optimization Methods and Software 28, no. 3 (June 2013): 424–441.
Author's final manuscript