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A Gentle, Geometric Introduction to Copositive Optimization

Samuel Burer (samuel-burer***at***uiowa.edu)

Abstract: This paper illustrates the fundamental connection between nonconvex quadratic optimization and copositive optimization---a connection that allows the reformulation of nonconvex quadratic problems as convex ones in a unified way. We intend the paper for readers new to the area, and hence the exposition is largely self-contained. We focus on examples having just a few variables or a few constraints for which the copositive problem itself can be recast in terms of linear, second-order-cone, and semidefinite optimization. A particular highlight is the role played by the geometry of the feasible set.

Keywords: copositive optimization, nonconvex quadratic optimization, semidefinite optimization, conic optimization

Category 1: Linear, Cone and Semidefinite Programming (Other )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation: Manuscript, Department of Management Sciences, University of Iowa, Iowa City, IA, USA, September 2014.

Download: [PDF]

Entry Submitted: 09/25/2014
Entry Accepted: 09/25/2014
Entry Last Modified: 01/17/2015

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