On augmented lagrangians for optimization problems with a single constraint
- Authors: Gasimov, Rafail , Rubinov, Alex
- Date: 2004
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 28, no. 2 (2004), p. 153-173
- Full Text: false
- Reviewed:
- Description: We examine augmented Lagrangians for optimization problems with a single (either inequality or equality) constraint. We establish some links between augmented Lagrangians and Lagrange-type functions and propose a new kind of Lagrange-type functions for a problem with a single inequality constraint. Finally, we discuss a supergradient algorithm for calculating optimal values of dual problems corresponding to some class of augmented Lagrangians.
- Description: C1
- Description: 2003000929
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