Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions

• 成果类型: Article
• 署名作者: Jeyakumar, V.; Rubinov, A. M.; Wu, Z. Y.
• 署名单位: University of New South Wales Sydney; Federation University Australia; Chongqing Normal University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-006-0012-5
• 发表日期: 2007
• 页码: 521-541
• 关键词: Optimization

摘要

In this paper, we first examine how global optimality of non-convex constrained optimization problems is related to Lagrange multiplier conditions. We then establish Lagrange multiplier conditions for global optimality of general quadratic minimization problems with quadratic constraints. We also obtain necessary global optimality conditions, which are different from the Lagrange multiplier conditions for special classes of quadratic optimization problems. These classes include weighted least squares with ellipsoidal constraints, and quadratic minimization with binary constraints. We discuss examples which demonstrate that our optimality conditions can effectively be used for identifying global minimizers of certain multi-extremal non-convex quadratic optimization problems.