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 rder cone constraint and two special linear constraints.

Key words: Linear conic program , Semidefinite program , Nonconvex quadratically, constrained quadratic program , Second-order cone