Partially Asynchronous, Parallel Algorithms for Network Flow and Other Problems

The problem of computing a fixed point of a nonexpansive function $f$ is considered. Sufficient conditions are provided under which a parallel, partially asynchronous implementation of the iteration $x: = f(x)$ converges. These results are then applied to (i) quadratic programming subject to box con...

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Published inSIAM journal on control and optimization Vol. 28; no. 3; pp. 678 - 710
Main Authors Tseng, P., Bertsekas, D. P., Tsitsiklis, J. N.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.03.1990
Subjects
Agreements
Algorithms
Applied sciences
Exact sciences and technology
Markov analysis
Network management systems
Operational research and scientific management
Operational research. Management science
Optimization
Optimization. Search problems
Parallel algorithm
Sufficient condition
Asynchronism
Jacobi method
Simulation
Network flow
Neural network
Quadratic programming
Gauss Seidel method
Optimization
Convergence
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Summary:The problem of computing a fixed point of a nonexpansive function $f$ is considered. Sufficient conditions are provided under which a parallel, partially asynchronous implementation of the iteration $x: = f(x)$ converges. These results are then applied to (i) quadratic programming subject to box constraints, (ii) strictly convex cost network flow optimization, (iii) an agreement and a Markov chain problem, (iv) neural network optimization, and (v) finding the least element of a polyhedral set determined by a weakly diagonally dominant, Leontief system. Finally, simulation results illustrating the attainable speedup and the effects of asynchronism are presented.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0363-0129
1095-7138
DOI:10.1137/0328040