Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming
The augmented Lagrangian method can be used for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The augmented Lagrangian objective function of a stochastic linear problem is not twice differentiable which precludes the use of...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/735916 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850171420532801536 |
|---|---|
| author | Saeed Ketabchi Malihe Behboodi-Kahoo |
| author_facet | Saeed Ketabchi Malihe Behboodi-Kahoo |
| author_sort | Saeed Ketabchi |
| collection | DOAJ |
| description | The augmented Lagrangian method can be used for solving recourse problems
and obtaining their normal solution in solving two-stage stochastic linear
programming problems. The augmented Lagrangian objective function of
a stochastic linear problem is not twice differentiable which precludes the
use of a Newton method. In this paper, we apply the smoothing techniques
and a fast Newton-Armijo algorithm for solving an unconstrained smooth
reformulation of this problem. Computational results and comparisons are
given to show the effectiveness and speed of the algorithm. |
| format | Article |
| id | doaj-art-9c01a267ba4c49458b7c126da0e55a39 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9c01a267ba4c49458b7c126da0e55a392025-08-20T02:20:16ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/735916735916Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear ProgrammingSaeed Ketabchi0Malihe Behboodi-Kahoo1Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 416351914 Rasht, IranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 416351914 Rasht, IranThe augmented Lagrangian method can be used for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The augmented Lagrangian objective function of a stochastic linear problem is not twice differentiable which precludes the use of a Newton method. In this paper, we apply the smoothing techniques and a fast Newton-Armijo algorithm for solving an unconstrained smooth reformulation of this problem. Computational results and comparisons are given to show the effectiveness and speed of the algorithm.http://dx.doi.org/10.1155/2013/735916 |
| spellingShingle | Saeed Ketabchi Malihe Behboodi-Kahoo Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming Journal of Applied Mathematics |
| title | Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming |
| title_full | Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming |
| title_fullStr | Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming |
| title_full_unstemmed | Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming |
| title_short | Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming |
| title_sort | smoothing techniques and augmented lagrangian method for recourse problem of two stage stochastic linear programming |
| url | http://dx.doi.org/10.1155/2013/735916 |
| work_keys_str_mv | AT saeedketabchi smoothingtechniquesandaugmentedlagrangianmethodforrecourseproblemoftwostagestochasticlinearprogramming AT malihebehboodikahoo smoothingtechniquesandaugmentedlagrangianmethodforrecourseproblemoftwostagestochasticlinearprogramming |