Parallel bundle-based decomposition for large-scale structured mathematical programming problems
Annals of Operations Research
Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
Alternating direction splittings for block angular parallel optimization
Journal of Optimization Theory and Applications
Primal-dual interior-point methods
Primal-dual interior-point methods
A Parallel Interior Point Method and Its Application to Facility Location Problems
Computational Optimization and Applications
Parallel and Distributed Computation: Numerical Methods
Parallel and Distributed Computation: Numerical Methods
Progress Made in Solving the Multicommodity Flow Problem
SIAM Journal on Optimization
A Specialized Interior-Point Algorithm for Multicommodity Network Flows
SIAM Journal on Optimization
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
A Bundle Type Dual-Ascent Approach to Linear Multicommodity Min-Cost Flow Problems
INFORMS Journal on Computing
Top500 Supercomputer Sites
INFORMS Journal on Computing
Gigaflops in linear programming
Operations Research Letters
Hi-index | 0.00 |
A parallel implementation of the specialized interior-point algorithm for multicommodity network flows introduced in [5] is presented. In this algorithm, the positive definite systems of each iteration are solved through a scheme that combines direct factorization and a preconditioned conjugate gradient (PCG) method. Since the solution of at least k independent linear systems is required at each iteration of the PCG, k being the number of commodities, a coarse-grained parallellization of the algorithm naturally arises. Also, several other minor steps of the algorithm are easily parallelized by commodity. An extensive set of computational results on a shared memory machine is presented, using problems of up to 2.5 million variables and 260,000 constraints. The results show that the approach is especially competitive on large, difficult multicommodity flow problems.