Quadratic optimization over one first-order cone

Xiaoling Guo; Zhibin Deng; Shu-Cherng Fang; Wenxun Xing

doi:10.3934/jimo.2014.10.945

Article Contents

2014, Volume 10, Issue 3: 945-963. Doi: 10.3934/jimo.2014.10.945

This issue Previous Article Finite-time optimal consensus control for second-order multi-agent systems Next Article A majorized penalty approach to inverse linear second order cone programming problems

Quadratic optimization over one first-order cone

1.
Department of Mathematical Sciences, Tsinghua University, Beijing, 100084
2.
Industrial and Systems Engineering Department, North Carolina State University, Raleigh, NC 27695-7906

Received: January 31, 2013

Revised: May 31, 2013

Published: June 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C20, 90C26; Secondary: 15B48, 65Y20.

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