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A gentle, geometric introduction to copositive optimization

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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 focus on examples having just a few variables or a few constraints for which the quadratic problem can be formulated as a copositive-style problem, which 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.

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Acknowledgments

The author expresses his sincere thanks to three anonymous referees for comments and insights that have greatly improved the paper.

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  1. Department of Management Sciences, University of Iowa, Iowa City, IA, 52242–1994, USA

    Samuel Burer

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  1. Samuel Burer
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Correspondence to Samuel Burer.

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Burer, S. A gentle, geometric introduction to copositive optimization. Math. Program. 151, 89–116 (2015). https://doi.org/10.1007/s10107-015-0888-z

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  • DOI: https://doi.org/10.1007/s10107-015-0888-z

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