A geometric characterization of strong duality in nonconvex quadratic programming with linear and nonconvex quadratic constraints

• 成果类型: Article
• 署名作者: Flores-Bazan, Fabian; Carcamo, Gabriel
• 署名单位: Universidad de Concepcion; Universidad de Concepcion
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0647-y
• 发表日期: 2014
• 页码: 263-290
• 关键词: Existence; THEOREMS; EXTENSIONS; convexity; interior; minima; lemma

摘要

We first establish a relaxed version of Dines theorem associated to quadratic minimization problems with finitely many linear equality and a single (nonconvex) quadratic inequality constraints. The case of unbounded optimal valued is also discussed. Then, we characterize geometrically the strong duality, and some relationships with the conditions employed in Finsler theorem are established. Furthermore, necessary and sufficient optimality conditions with or without the Slater assumption are derived. Our results can be used to situations where none of the results appearing elsewhere are applicable. In addition, a revisited theorem due to Frank and Wolfe along with that due to Eaves is established for asymptotically linear sets.