An augmented Lagrangian decomposition method for block diagonal linear programming problems

1989 ◽  
Vol 8 (5) ◽  
pp. 287-294 ◽  
Author(s):  
Andrzej Ruszczyński
Keyword(s):  
Linear Programming ◽  
Decomposition Method ◽  
Augmented Lagrangian ◽  
Lagrangian Decomposition ◽  
Linear Programming Problems ◽  
Block Diagonal

scholarly journals Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Saeed Ketabchi ◽  
Malihe Behboodi-Kahoo
Keyword(s):  
Linear Programming ◽  
Augmented Lagrangian ◽  
Linear Problem ◽  
Augmented Lagrangian Method ◽  
Lagrangian Method ◽  
Stochastic Linear Programming ◽  
Two Stage ◽  
Smoothing Techniques ◽  
Linear Programming Problems ◽  
Recourse Problem

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.

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