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A Quadratically Constrained Quadratic Optimization Model for Completely Positive Cone Programming

Naohiko Arima (arima.n.ab***at***m.titech.ac.jp)
Sunyoung Kim (skim***at***ewha.ac.kr)
Masakazu Kojima (kojima***at***is.titech.ac.jp)

Abstract: We propose a class of quadratic optimization problems whose exact optimal objective values can be computed by their completely positive cone programming relaxations. The objective function can be any quadratic form. The constraints of each problem are described in terms of quadratic forms with no linear terms, and all constraints are homogeneous equalities, except one inhomogeneous equality where a quadratic form is set to be a positive constant. For the equality constraints, ``a hierarchy of copositvity" condition is assumed. This model is a generalization of the standard quadratic optimization problem of minimizing a quadratic form over the standard simplex, and covers many of the existing quadratic optimization problems studied for exact copositive cone and completely positive cone programming relaxations. In particular, it generalizes the recent results on quadratic optimization problems by Burer and the set-semidefinite representation by Eichfelder and Povh.

Keywords: Copositve programming, quadratic optimization problem with quadratic constraints, a hierarchy of copositivity.

Category 1: Linear, Cone and Semidefinite Programming

Citation: Research report B-468, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro-ku, Tokyo 152-8552 Japan

Download: [PDF]

Entry Submitted: 09/07/2012
Entry Accepted: 09/07/2012
Entry Last Modified: 09/07/2012

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