A new polynomial-time algorithm for linear programming
Combinatorica
A regularized decomposition method for minimizing a sum of polyhedral functions
Mathematical Programming: Series A and B
A polynomial-time algorithm, based on Newton's method, for linear programming
Mathematical Programming: Series A and B
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Nondifferentiable optimization
Optimization
Solving combinatorial optimization problems using Karmakar's algorithm
Mathematical Programming: Series A and B
Parallel decomposition of multistage stochastic programming problems
Mathematical Programming: Series A and B
Multicommodity network flows: the impact of formulation on decomposition
Mathematical Programming: Series A and B
PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
A cutting plane method from analytic centers for stochastic programming
Mathematical Programming: Series A and B
New variants of bundle methods
Mathematical Programming: Series A and B
Solving nonlinear multicommodity flow problems by the analytic center cutting plane method
Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
MPI: The Complete Reference
Warm Start and ε-Subgradients in a Cutting Plane Scheme
Computational Optimization and Applications
Dynamic Nonlinear Modelization of Operational Supply Chain Systems
Journal of Global Optimization
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We use a decomposition approach to solve three types of realistic problems: block-angular linear programs arising in energy planning, Markov decision problems arising in production planning and multicommodity network problems arising in capacity planning for survivable telecommunication networks. Decomposition is an algorithmic device that breaks down computations into several independent subproblems. It is thus ideally suited to parallel implementation. To achieve robustness and greater reliability in the performance of the decomposition algorithm, we use the Analytic Center Cutting Plane Method (ACCPM) to handle the master program. We run the algorithm on two different parallel computing platforms: a network of PC's running under Linux and a genuine parallel machine, the IBM SP2. The approach is well adapted for this coarse grain parallelism and the results display good speed-up's for the classes of problems we have treated.