List of Titles

Authors: Rubinov, Alex , Yang, Xiao , Bagirov, Adil , Gasimov, Rafail
Date: 2003
Type: Text , Journal article
Relation: Journal of Mathematical Sciences Vol. 115, no. 4 (2003), p. 2437-2505
Full Text: false
Reviewed:
Description: We examine various kinds of nonlinear Lagrange-type functions for constrained optimization problems. In particular, we study the weak duality, the zero duality gap property, and the existence of an exact parameter for these functions. The paper contains a detailed survey of results in these directions and comparison of different methods proposed by different authors. Some new results are also given.
Description: C1
Description: 2003000358

Authors: Burachik, Regina , Gasimov, Rafail , Ismayilova, Nergiz , Kaya, Yalcin
Date: 2006
Type: Text , Journal article
Relation: Journal of Global Optimization Vol. 34, no. 1 (2006), p. 55-78
Full Text: false
Reviewed:
Description: We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem
Description: C1
Description: 2003002552

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

Authors: Rubinov, Alex , Gasimov, Rafail
Date: 2004
Type: Text , Journal article
Relation: Journal of Global Optimization Vol. 29, no. 4 (2004), p. 455-477
Full Text: false
Reviewed:
Description: We consider problems of vector optimization with preferences that are not necessarily a pre-order relation. We introduce the class of functions which can serve for a scalarization of these problems and consider a scalar duality based on recently developed methods for non-linear penalization scalar problems with a single constraint.
Description: C1
Description: 2003000932

Authors: Rubinov, Alex , Gasimov, Rafail
Date: 2003
Type: Text , Journal article
Relation: Optimization Vol. 52, no. 1 (2003), p. 1-28
Full Text: false
Reviewed:
Description: We study a nonlinear exact penalization for optimization problems with a single constraint. The penalty function is constructed as a convolution of the objective function and the constraint by means of increasing positively homogeneous (IPH) functions. The main results are obtained for penalization by strictly IPH functions. We show that some restrictive assumptions, which have been made in earlier researches on this topic, can be removed. We also compare the least exact penalty parameters for penalization by different convolution functions. These results are based on some properties of strictly IPH functions that are established in the article.
Description: C1
Description: 2003000357

Authors: Rubinov, Alex , Gasimov, Rafail
Date: 2002
Type: Text , Journal article
Relation: Applied and Computational Mathematics Vol. 1, no. 2 (2002), p. 142-157
Full Text: false
Reviewed:
Description: The paper contains the survey of some recent results obtained by the authors and their colleagues. We study zero duality gap properties for optimization problems with a single constraint with respect to a nonlinear penalization. The penalty function is constructed as a convolution of the objective function and the constraint by means of IPH (increasing positively homogeneous) functions. The main results are obtained for penalization by strictly IPH functions. We also examine augmented Lagrangians for optimization problems with a single constraint. We establish some links between augmented Lagrangians and Lagrange-type functions and propose a new kind of Lagrange-type functions for the problems with a single inequality constraint.
Description: C1
Description: 2003000115

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