2014 journal article

QUADRATIC OPTIMIZATION OVER ONE FIRST-ORDER CONE

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 10(3), 945–963.

By: X. Guo, Z. Deng*, S. Fang* & W. Xing

author keywords: Quadratic programming; cone of nonnegative quadratic forms; first-order cone; linear conic programming; adaptive scheme
Source: Web Of Science
Added: August 6, 2018

This paper studies the first-order cone constrained homogeneous quadratic programming problem. For efficient computation, the problem is reformulated as a linear conic programming problem. A union of second-order cones are designed to cover the first-order cone such that a sequence of linear conic programming problems can be constructed to approximate the conic reformulation. Since the cone of nonnegative quadratic forms over a union of second-order cones has a linear matrix inequalities representation, each linear conic programming problem in the sequence is polynomial-time solvable by applying semidefinite programming techniques. The convergence of the sequence is guaranteed when the union of second-order cones gets close enough to the first-order cone. In order to further improve the efficiency, an adaptive scheme is adopted. Numerical experiments are provided to illustrate the efficiency of the proposed approach.