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

Column Generation within the L-shaped Method for Stochastic Linear Programs

We develop a method that incorporates column generation within the Lshaped method for solving two-stage stochastic linear programs. This method adds feasibility and optimality cuts generated from the second-stage subproblems based on the current columns in the master problem of the L-shaped method. It also generates columns for the master problem with respect to the first-stage constraints as w...

A Parallel BFGS-SQP Method for Stochastic Linear Programs

A Parallel Interior Point Method for Stochastic Linear Programs

This paper describes a parallel implementation of the primal-dual interior point method for a special class of large linear programs that occur in stochastic linear programming. The method used by Vanderbei and Carpenter [31] for removing dense columns is modi ed to eliminate variables which link blocks in stochastic linear programs. The algorithm developed was tested on six test problems from ...

A smoothing augmented Lagrangian method for solving simple bilevel programs

In this paper, we design a numerical algorithm for solving a simple bilevel program where the lower level program is a nonconvex minimization problem with a convex set constraint. We propose to solve a combined problem where the first order condition and the value function are both present in the constraints. Since the value function is in general nonsmooth, the combined problem is in general a...

Augmented Lagrangian Filter Method∗

We introduce a filter mechanism to force convergence for augmented Lagrangian methods for nonlinear programming. In contrast to traditional augmented Lagrangian methods, our approach does not require the use of forcing sequences that drive the first-order error to zero. Instead, we employ a filter to drive the optimality measures to zero. Our algorithm is flexible in the sense that it allows fo...