A gentle, geometric introduction to copositive optimization

• 成果类型: Article; Proceedings Paper
• 署名作者: Burer, Samuel
• 署名单位: University of Iowa
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0888-z
• 发表日期: 2015
• 页码: 89-116
• 关键词: representations; constraints; matrices; PROGRAMS

摘要

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.