scholarly journals Serial and Parallel Solution of Large Scale Linear Programs by Augmented Lagrangian Successive Overrelaxation

1988 ◽  
pp. 103-124 ◽  
Author(s):  
R. De Leone ◽  
O. L. Mangasarian
Keyword(s):  
Large Scale ◽  
Augmented Lagrangian ◽  
Linear Programs ◽  
Successive Overrelaxation ◽  
Parallel Solution

scholarly journals Parallel implementation of augmented Lagrangian method within L-shaped method for stochastic linear programs

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 799-808
Author(s):  
Malihe Behboodi-Kahoo ◽  
Saeed Ketabchi
Keyword(s):  
Large Scale ◽  
Augmented Lagrangian ◽  
Parallel Implementation ◽  
Augmented Lagrangian Method ◽  
Lagrangian Method ◽  
Quadratic Functions ◽  
Maximization Problem ◽  
Linear Programs ◽  
Parallel Method ◽  
Generalized Newton

In this paper, we study two-stage stochastic linear programming (SLP) problems with fixed recourse. The problem is often large scale as the objective function involves an expectation over a discrete set of scenarios. This paper presents a parallel implementation of the augmented Lagrangian method for solving SLPs. Our parallel method is based on a modified version of the L-shaped method and reducing linear master and recourse programs to unconstrained maximization of concave differentiable piecewise quadratic functions. The maximization problem is solved using the generalized Newton method. The parallel method is implemented in MATLAB. Large scale SLP with several millions of variables and several hundreds of thousands of constraints are solved. The results of uniprocessor and multiprocessor computations are presented which show that the parallel algorithm is effective.

Parallel solution of large-scale, block-angular linear programs

1990 ◽  
Vol 22 (1) ◽  
pp. 23-41 ◽  
Author(s):  
J. B. Rosen ◽  
Robert S. Maier
Keyword(s):  
Large Scale ◽  
Linear Programs ◽  
Parallel Solution

Parallel Solution of Large-Scale and Sparse Generalized Algebraic Riccati Equations

2006 ◽  
pp. 710-719 ◽  
Author(s):  
José M. Badía ◽  
Peter Benner ◽  
Rafael Mayo ◽  
Enrique S. Quintana-Ortí
Keyword(s):  
Large Scale ◽  
Riccati Equations ◽  
Parallel Solution ◽  
Algebraic Riccati Equations
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