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

For linear optimization types 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 offers a sublime framework of resolution algorithms in addition to fiscal interpretation. This monograph is the whole documentation of DECOMP: a strong implementation of the Dantzig-Wolfe decomposition process in FORTRAN. The code can function a truly handy place to begin for additional research, either computational and monetary, of parallelism in large-scale platforms. it may well even be used as supplemental fabric in a moment direction in linear programming, computational mathematical programming, or large-scale systems.

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**Additional info for DECOMP: an Implementation of Dantzig-Wolfe Decomposition for Linear Programming**

**Sample text**

2. In the absence of basic equality logicals, to remove as many infeasibilities as possible if there are any remaining infeasibilities. 54 Since the rhs is not necessarily positive, some changes as illustrated in the example below will have to be made to the normal RSM ratio test. 22) -9x1 Here a1 and a2 are equality logicals, x2 to x5 are variables that are not equality logicals and xl is the entering variable. The following observations can be made with this example. 1. 22) cannot be ignored.

C '1' indicates step 2 of D-W Phase 1 or D-W Phase 2. '3' indicates D-W C Phase 3. C MSTAT C DX C C Indicates status of the problem. Subproblem objective value minus the dual variable of the corresponding convexity constraint. DX is the reduced cost of the proposal column. KRIT(*): Indicates the type of the strategy chosen by the user. '2' if intermediate C proposals are allowed. '1' if proposals only at optimality of unboundedness C of the subproblem. C LSUB Indicates problem index. '0' for master problem.

Lines 56 - 59] - Set KFASE to 1 and call FORMC. 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(*, *).