On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

Authors:
Regina S. Burachik;Rafail N. Gasimov;Nergiz A. Ismayilova;C. Yalçin. Kaya
Affiliations:
Engenharia de Sistemas e Computação, COPPE-UFRJ, Rio de Janeiro-RJ, Brazil CEP 21941-972;Department of Industrial Engineering, Osmangazi University, Eskişehir, Turkey 26030;Department of Industrial Engineering, Osmangazi University, Eskişehir, Turkey 26030;School of Mathematics and Statistics, University of South Australia, Mawson Lakes, Australia 5095
Venue:
Journal of Global Optimization
Year:
2006

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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.