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 sustaining subproblems with coupling constraints, the Dantzig-Wolfe decomposition precept offers a sublime framework of resolution algorithms in addition to monetary interpretation. This monograph is the whole documentation of DECOMP: a powerful implementation of the Dantzig-Wolfe decomposition technique in FORTRAN. The code can function a really handy place to begin for additional research, either computational and financial, of parallelism in large-scale structures. it might probably even be used as supplemental fabric in a moment path in linear programming, computational mathematical programming, or large-scale systems.
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Additional resources for DECOMP: an Implementation of Dantzig-Wolfe Decomposition for Linear Programming
If the solution is infeasible then C since KFASE is 1, FORMC would already have set up the cost vector in C the buffer YA(*, 5). Otherwise set KF ASE to 2 and call FORMC again C to set up the cost vector in YA(*, 6). [lines 60 - 69] C C - Write the proposal into Z(*, *) and the reduced cost of the proposal column in the (NROWO+ 1)st row of Z(*, *). [lines 70 - 72] 46 C C C C C C column of Z(*, *). [lines 53 - 55] - If KSTR is not 5 and there is space in Z(*, *) then write the current proposal to the ftrst available colurnn of Z(*, *).
Solving the master and subproblems with RSM. 2. b. Data handling to update and solve the master and subproblems. 1. c. 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.
Determine which proposal tests, if any, have to be done. 2. Perform (a) Test A, Test B, Percentage Test and Frequency Test; or (b) Termination Test as is appropriate. 3. Incorporate (a) an extreme point proposal; or 42 (b) an extreme ray proposal and thereafter. possibly an extreme point proposal. 8 Detailed Comments C************************************************************************* C Step 1 : CHECK C C MAST Indicates stage of the problem. '0' indicates step 1 of D-W Phase 1. C '1' indicates step 2 of D-W Phase 1 or D-W Phase 2.