Quadratic Optimization over a Second-Order Cone with Linear Equality Constraints

Abstract

This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality constraints. When the feasible region is bounded, we show that an optimal solution of the problem can be found in polynomial time. When the feasible region is unbounded, a semidefinite programming (SDP) reformulation is constructed to find the optimal objective value of the original problem in polynomial time. In addition, we provide two sufficient conditions, under which, if the optimal objective value is finite, we show the optimal solution of SDP reformulation can be decomposed into the original space to generate an optimal solution of the original problem in polynomial time. Otherwise, a recession direction can be identified in polynomial time. Numerical examples are included to illustrate the effectiveness of the proposed approach.