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
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
- Full Text: false
- 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
Generalized Fenchel's conjugation formulas and duality for abstract convex functions
- Authors: Jeyakumar, Vaithilingam , Rubinov, Alex , Wu, Zhiyou
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 132, no. 3 (Mar 2007), p. 441-458
- Full Text: false
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- Description: In this paper, we present a generalization of Fenchel's conjugation and derive infimal convolution formulas, duality and subdifferential (and epsilon-subdifferential) sum formulas for abstract convex functions. The class of abstract convex functions covers very broad classes of nonconvex functions. A nonaffine global support function technique and an extended sum- epiconjugate technique of convex functions play a crucial role in deriving the results for abstract convex functions. An additivity condition involving global support sets serves as a constraint qualification for the duality.
- Description: C1
Sufficient global optimality conditions for non-convex quadratic minimization problems with box constraints
- Authors: Jeyakumar, Vaithilingam , Rubinov, Alex , Wu, Zhiyou
- Date: 2006
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 36, no. 3 (2006), p. 471-481
- Full Text: false
- Reviewed:
- Description: In this paper we establish conditions which ensure that a feasible point is a global minimizer of a quadratic minimization problem subject to box constraints or binary constraints. In particular, we show that our conditions provide a complete characterization of global optimality for non-convex weighted least squares minimization problems. We present a new approach which makes use of a global subdifferential. It is formed by a set of functions which are not necessarily linear functions, and it enjoys explicit descriptions for quadratic functions. We also provide numerical examples to illustrate our optimality conditions.
- Description: C1
- Description: 2003001538