Strengthening Semidefinite Programming Relaxations of Polynomial Optimization Problems

Abstract

Solving polynomial optimization problems (POPs) has become an essential subject in recent developments. When large scale POPs are solved using the branch-and-bound method, it is necessary to have proper convex relaxations for the framework of the branch-and-bound method. Semidefinite program (SDP) relaxations suitable to the framework of branch-and-bound method are proposed. We add linear constraints obtained by partitioning the feasible region into the Cartesian product of two-dimensional triangles and rectangles. The usefulness of these new relaxation is demonstrated computationally.