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On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian* |
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| Authors: | Regina S Burachik Rafail N Gasimov Nergiz A Ismayilova C Yalçin Kaya |
| Institution: | 1. Engenharia de Sistemas e Computa??o, COPPE-UFRJ, CP 68511, Rio de Janeiro-RJ, CEP 21941-972, Brazil 3. Department of Industrial Engineering, Osmangazi University, Bademlik, 26030, Eski?ehir, Turkey 2. Department of Industrial Engineering, Osmangazi University, Bademlik, 26030, Eski?ehir, Turkey 4. School of Mathematics and Statistics, University of South Australia, Mawson Lakes, S.A., 5095, Australia |
| Abstract: | 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. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA. |
| Keywords: | Augmented Lagrangian Nonconvex programming Nonsmooth optimization Sharp Lagrangian Subgradient optimization |
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