Parallel implementation of Newton’s method for solving large-scale linear programs

Parallel versions of a method based on reducing a linear program (LP) to an unconstrained maximization of a concave differentiable piecewise quadratic function are proposed. The maximization problem is solved using the generalized Newton method. The parallel method is implemented in C using the MPI...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 49; no. 8; pp. 1303 - 1317
Main Authors: Garanzha, V. A., Golikov, A. I., Evtushenko, Yu. G., Nguen, M. Kh
Format: Journal Article
Language:English
Published: Dordrecht SP MAIK Nauka/Interperiodica 01.08.2009
Springer Nature B.V
Subjects:
Computational mathematics
Computational Mathematics and Numerical Analysis
Linear programming
Mathematics
Mathematics and Statistics
Optimization
Studies
linear programming
generalized Newton’s method
unconstrained optimization
parallel computations
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:Parallel versions of a method based on reducing a linear program (LP) to an unconstrained maximization of a concave differentiable piecewise quadratic function are proposed. The maximization problem is solved using the generalized Newton method. The parallel method is implemented in C using the MPI library for interprocessor data exchange. Computations were performed on the parallel cluster MVC-6000IM. Large-scale LPs with several millions of variables and several hundreds of thousands of constraints were solved. Results of uniprocessor and multiprocessor computations are presented.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S096554250908003X