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  • 1
    Electronic Resource
    Electronic Resource
    Load balancing in the parallel optimization of block-angular linear programs (1993)
    Springer
    Mathematical programming 62 (1993), S. 41-67 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; Dantzig—Wolfe decomposition ; large-scale systems ; parallel processing ; hypercube architecture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Decomposition algorithms for block-angular linear programs give rise to a natural, coarse-grained parallelism that can be exploited by processing the subproblems concurrently within a distributed-memory environment. The parallel efficiency of the distributed approach, however, is critically dependent on the duration of the inherently serial master phase relative to that of the bottleneck subproblem. This paper investigates strategies for improving efficiency in distributed Dantzig—Wolfe decomposition by better balancing the load between the master and subproblem processors. We report computational experience on an Intel iPSC/2 hypercube multiprocessor with test problems having dimensions up to about 30 000 rows, 87 000 columns, and 200 coupling constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585159
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A set of staircase linear programming test problems (1981)
    Springer
    Mathematical programming 20 (1981), S. 245-250 
    Details
    ISSN: 1436-4646
    Keywords: Staircase Linear Programs ; Test Problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A set of staircase linear programming test problems are made available for computational experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589349
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Decomposition of linear programs using parallel computation (1988)
    Springer
    Mathematical programming 42 (1988), S. 391-405 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; large-scale-systems ; decomposition ; parallel computing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes DECOMPAR: an implementation of the Dantzig-Wolfe decomposition algorithm for block-angular linear programs using parallel processing of the subproblems. The software is based on a robust experimental code for LP decomposition and runs on the CRYSTAL multicomputer at the University of Wisconsin-Madison. Initial computational experience is reported. Promising directions in future development of this approach are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589413
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    An advanced implementation of the Dantzig—Wolfe decomposition algorithm for linear programming (1981)
    Springer
    Mathematical programming 20 (1981), S. 303-326 
    Details
    ISSN: 1436-4646
    Keywords: Large-Scale Systems ; Decomposition Algorithms ; Structured Linear Programs ; Optimization Software
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Since the original work of Dantzig and Wolfe in 1960, the idea of decomposition has persisted as an attractive approach to large-scale linear programming. However, empirical experience reported in the literature over the years has not been encouraging enough to stimulate practical application. Recent experiments indicate that much improvement is possible through advanced implementations and careful selection of computational strategies. This paper describes such an effort based on state-of-the-art, modular linear programming software (IBM's MPSX/370).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589355
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Nested decomposition for dynamic models (1974)
    Springer
    Mathematical programming 6 (1974), S. 121-140 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This nested decomposition algorithm is intended for solving linear programs with the staircase structure that is characteristic of dynamic multi-sector models for economic development. Staircase problems represent a special case of the discrete-time optimal control problem. Our method is based upon the same principles as that of Glassey [5], but appears easier to describe and to relate to control theory. Computational experience is reported for a series of test problems. The algorithm has been coded in MPL, an experimental language for mathematical programming. This translator has made it possible to obtain a more readable program — and with fewer instructions — than one written in a conventional language. However, because the present version of MPL does not permit the use of slow access memory, this has prevented us from exploring the full potential of nested decomposition for solving larger problems than can be handled by conventional simplex techniques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580231
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    On the efficacy of distributed simplex algorithms for linear programming (1994)
    Springer
    Computational optimization and applications 3 (1994), S. 349-363 
    Details
    ISSN: 1573-2894
    Keywords: Linear programming ; distributed computation ; multiprocessing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider the use of distributed computation to solve general unstructured linear programs by the inherently serial approach of the simplex method. Timing models for the distributed algorithms are presented to predict results which are then verified empirically. Our results contribute to the identification of all viable exploitations of distributed computing which is likely to become a prevalent environment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01299209
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    Paper (German National Licenses)
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