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  • 1
    Electronic Resource
    Electronic Resource
    Decomposition in large system optimization using the method of multipliers (1978)
    Springer
    Journal of optimization theory and applications 25 (1978), S. 181-193 
    Details
    ISSN: 1573-2878
    Keywords: Decomposition techniques ; generalized Lagrangian ; large system optimization ; method of multipliers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Although the method of multipliers can resolve the dual gaps which will often appear between the true optimum point and the saddle point of the Lagrangian in large system optimization using the Lagrangian approach, it is impossible to decompose the generalized Lagrangian in a straightforward manner because of its quadratic character. A technique using the linear approximation of the perturbed generalized Lagrangian has recently been proposed by Stephanopoulos and Westerberg for the decomposition. In this paper, another attractive decomposition technique which transforms the nonseparable crossproduct terms into the minimum of sum of separable terms is proposed. The computational efforts required for large system optimization can be much reduced by adopting the latter technique in place of the former, as illustrated by application of these two techniques to an optimization problem of a chemical reactor system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933211
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    An infeasible method of large-system optimization by direct coordination of subsystem inputs (1978)
    Springer
    Journal of optimization theory and applications 24 (1978), S. 437-448 
    Details
    ISSN: 1573-2878
    Keywords: Decomposition techniques ; generalized Lagrangian ; large-systems optimization ; method of multipliers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An infeasible method of large-system optimization is proposed. The dual gap is resolved by use of the generalized Lagrangian as in the previous methods due to Stephanopouloset al. and Watanabeet al. The values of subsystem inputs are, however, coordinated in the second level, instead of being adjusted in the first level, as in previous methods. As a result, in contrast with previous methods, the subproblems in the first level include a small number of variables to be adjusted; in addition, the generalized Lagrangian is decomposable in a simple manner. Further, the decomposition is not subject to any restriction, which is often encountered in feasible methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932887
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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