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- W2017069611 abstract "Degeneracy may cause various computing and other complications in any mathematical programming problem of the kind where the constraint set defines a convex polyhedral set (particularly, a polytope). In order to be able to study various seemingly independent degeneracy phenomena from a unifying viewpoint a so-called degeneracy graph (DG for short) is defined, and its properties analysed. Cycling of the simplex method for LP is analysed and a method to construct cycling examples of arbitrary size is proposed. The neighbourhood problem is solved by a new approach to determine a minimal N-tree (N for neighbour), and an efficient method to determine all vertices of a convex polytope is described. A new version of the simplex method is indicated that does not need Phase 1, should be faster than commercial codes and automatically contains an anticycling device. For a degenerate optimal solution of an LP-problem, sensitivity analysis as well as shadow price determination and interpretation are tackled by using a special class of DG's, the so-called optimum DG's. The connection between weakly redundant constraints, a degenerate optimal solution of the associated LP and sensitivity analysis as well as shadow price determination is analysed." @default.
- W2017069611 created "2016-06-24" @default.
- W2017069611 creator A5039513667 @default.
- W2017069611 date "2003-12-01" @default.
- W2017069611 modified "2023-09-26" @default.
- W2017069611 title "Degeneracy problems in mathematical programming and degeneracy graphs" @default.
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- W2017069611 doi "https://doi.org/10.5784/6-1-478" @default.
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