DECOMP: an Implementation of Dantzig-Wolfe Decomposition for by Professor James K. Ho, Professor Rangaraja P. Sundarraj

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By Professor James K. Ho, Professor Rangaraja P. Sundarraj (auth.)

For linear optimization versions that may be formulated as linear courses with the block-angular constitution, i.e. self sufficient subproblems with coupling constraints, the Dantzig-Wolfe decomposition precept presents a sublime framework of answer algorithms in addition to monetary interpretation. This monograph is the total documentation of DECOMP: a powerful implementation of the Dantzig-Wolfe decomposition process in FORTRAN. The code can function a truly handy start line for extra research, either computational and financial, of parallelism in large-scale structures. it might probably even be used as supplemental fabric in a moment direction in linear programming, computational mathematical programming, or large-scale systems.

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2. 1. 65) changes from cycle to cycle. However, with the column packing scheme for sparse matrices, it is not convenient to compute and store the objective function explicitly which would involve the insertion and deletion of nonzero elements. Moreover, generating a proposal by multiplying xr explicitly by AIr would require a distinction among the AIr and A2r data stored compactly in the proposed data structure. Both of these difficulties can be overcome with the following method. Recall that in RSM the objective function is required only for finding the reduced cost.

K) the only element that changes in c'B is the one corresponding to the pivot position of Ej and this element is computed by an inner product. Since the pivot element of each eta is stored first, the pivot position of the eta is readily inferred. 6. Detailed Comments C************************************************************************* BTRAN C C C NETA Number of etas generated. YA(*, *): Buffer, one of whose columns contains the cost vector. C C C C KVEC C u.. Indicates the column of Y A(*, *) containing the cost vector.

However, with the column packing scheme for sparse matrices, it is not convenient to compute and store the objective function explicitly which would involve the insertion and deletion of nonzero elements. Moreover, generating a proposal by multiplying xr explicitly by AIr would require a distinction among the AIr and A2r data stored compactly in the proposed data structure. Both of these difficulties can be overcome with the following method. Recall that in RSM the objective function is required only for finding the reduced cost.

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