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

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 ob...

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Bibliographic Details
Published in:Mathematical programming Vol. 110; no. 3; pp. 521 - 541
Main Authors: Jeyakumar, V., Rubinov, A. M., Wu, Z. Y.
Format: Journal Article
Language:English
Published: Heidelberg Springer 01.09.2007
Springer Nature B.V
Subjects:
Applied mathematics
Applied sciences
Constraints
Convex analysis
Exact sciences and technology
Information technology
Lagrange multiplier
Mathematical functions
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Quadratic programming
Studies
Non convex programming
Quadratic inequality constraints
Non-convex quadratic minimization
Constraint satisfaction
Minimization
Global optimum
Quadratic programming
Binary constraints
Convex programming
Constrained optimization
Lagrange multiplier
Global optimality conditions
Least squares method
Lagrange multipliers
Inequality constraint
Optimality condition
Optimality criterion
Ellipsoid
Non convex analysis
Mathematical programming
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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. [PUBLICATION ABSTRACT]
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-006-0012-5