Sufficient conditions for global optimality of bivalent nonconvex quadratic programs with inequality constraints
- Authors: Wu, Zhiyou , Jeyakumar, Vaithilingam , Rubinov, Alex
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 133, no. 1 (2007), p. 123-130
- Full Text: false
- Reviewed:
- Description: We present sufficient conditions for the global optimality of bivalent nonconvex quadratic programs involving quadratic inequality constraints as well as equality constraints. By employing the Lagrangian function, we extend the global subdifferential approach, developed recently in Jeyakumar et al. (J. Glob. Optim., 2007, to appear; Math. Program. Ser. A, 2007, to appear) for studying bivalent quadratic programs without quadratic constraints, and derive global optimality conditions. © 2007 Springer Science+Business Media, LLC.
- Description: C1
A filled function method for quadratic programs with binary constraints
- Authors: Wu, Zhiyou , Yang, Y. J. , Bai, Fusheng
- Date: 2009
- Type: Text , Journal article
- Relation: Optimization Vol. 58, no. 5 (2009), p. 585-598
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- Description: In this article, we first introduce a definition of a local minimizer for the quadratic programs with {-1, 1} constraints and show that the existing necessary condition of global optimality in some recent literature is in fact the necessary and sufficient condition of local optimality under the present definition. A filled function and the corresponding filled function algorithm then are proposed to get the global minimizer of the concerned minimization problem. The existing sufficient condition of global optimality is employed to form one of the termination rules of the algorithm. Several numerical examples are reported to show the efficiency of the present method for solving quadratic programs with binary constraints.
Non-convex quadratic minimization problems with quadratic constraints: Global optimality conditions
- Authors: Jeyakumar, Vaithilingam , Rubinov, Alex , Wu, Zhiyou
- Date: 2007
- Type: Text , Journal article
- Relation: Mathematical Programming Vol. 110, no. 3 (2007), p. 521-541
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- Reviewed:
- Description: 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. © Springer-Verlag 2007.
- Description: C1