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- Title
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions.
- Authors
Jeyakumar, V.; Rubinov, A. M.; Wu, Z. Y.
- Abstract
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.
- Subjects
NONCONVEX programming; MATHEMATICAL programming; CONSTRAINED optimization; MATHEMATICAL optimization; LAGRANGE equations
- Publication
Mathematical Programming, 2007, Vol 110, Issue 3, p521
- ISSN
0025-5610
- Publication type
Article
- DOI
10.1007/s10107-006-0012-5