A gentle, geometric introduction to copositive optimization

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.