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