Exact Computable Representation of Some Second-Order Cone Constrained Quadratic Programming Problems

Abstract

Solving the quadratically constrained quadratic programming (QCQP) problem is in general NP-hard. Only a few subclasses of the QCQP problem are known to be polynomial-time solvable. Recently, the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation, which reformulates the original problem as a linear semidefinite program with additional linear and second-order cone constraints. In this paper, we provide exact computable representations for some more subclasses of the QCQP problem, in particular, the subclass with one second-order cone constraint and two special linear constraints. © 2013 Operations Research Society of China, Periodicals Agency of Shanghai University, and Springer-Verlag Berlin Heidelberg.