Computable representation of the cone of nonnegative quadraticforms over a general second-order cone and its application tocompletely positive programming

Ye Tian; Shu-Cherng Fang; Zhibin Deng; Wenxun Xing

doi:10.3934/jimo.2013.9.703

Article Contents

2013, Volume 9, Issue 3: 703-721. Doi: 10.3934/jimo.2013.9.703

This issue Previous Article Convex hull of the orthogonal similarity set with applications in quadratic assignment problems Next Article

Computable representation of the cone of nonnegative quadratic forms over a general second-order cone and its application to completely positive programming

1.
School of Business Administration, Southwestern University of Finance and Economics, Chengdu, 611130
2.
Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27606
3.
Department of Mathematical Sciences, Tsinghua University, Beijing

Received: October 2012

Revised: February 2013

Published: July 2013

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Abstract

In this paper, we provide a computable representation of the cone of nonnegative quadratic forms over a general nontrivial second-order cone using linear matrix inequalities (LMI). By constructing a sequence of such computable cones over a union of second-order cones, an efficient algorithm is designed to find an approximate solution to a completely positive programming problem using semidefinite programming techniques. In order to accelerate the convergence of the approximation sequence, an adaptive scheme is adopted, and ``reformulation-linearization technique'' (RLT) constraints are added to further improve its efficiency.

Keywords:

Cone of nonnegative quadratic forms general nontrivial second-order cone completely positive programming approximation adaptive scheme.

Mathematics Subject Classification: Primary: 90C26, 90C59, 90C22; Secondary: 30E10.

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