Second Order Cone Relaxation of Polynomial Optimization Problems with the Ball Constraint

Abstract

Solving polynomial optimization problems(POPs) over cones has become anessential subject in recent developments. The second order cone programming(SOCP) relaxation methods have been known for efficiency when providing lower bounds for optimal values of POPs. We present a new SOCP relaxation that can give the exact optimal object values for POPs of diagonally dominant coefficient matrix if ball constraint is added. Key words. polynomial optimization problems, semidefinite program, second order cone program, quadratic program, ball constraint.