An Accelerated First-Order Method for Solving Unconstrained Polynomial Optimization Problems

Our interest lies in solving 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 behavior of the first-order method for unconstrained polynomial optimization.