Abstract
This paper describes a partitioning method for solving a class of structured nonlinear programming problems with block diagonal constraints and a few coupling variables.
The special structure of the constraints is used to reduce the given problem by elimination of variables. In variance to other methods proposed previously, this elimination is effected through the use of the general solution to an underdetermined system of linear equations representing the active constraints at a given feasible point. For weakly coupled systems, this arrangement provides a drastic reduction in the number of variables. The solution to the overall problem is obtained by solving a sequence of the reduced nonlinear programs. Primal feasibility is maintained throughout the optimization procedure. Computational experience and results are presented.
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This work was supported in part by the National Science Foundation under Research Grant GJ-0362 and in part by the New York Scientific Center, IBM Corporation.
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Grigoriadis, M.D. A projective method for structured nonlinear programs. Mathematical Programming 1, 321–358 (1971). https://doi.org/10.1007/BF01584096
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DOI: https://doi.org/10.1007/BF01584096