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.

Key words: Quadratic programming , Linear conic programming , Second-order
cone , Cone of nonnegative quadratic functions