Degeneracy Graphs and Simplex Cycling (Lecture Notes in Economics and Mathematical Systems, Band 357)
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Beschreibung
Many problems in economics can be formulated as linearly constrained mathematical optimization problems, where the feasible solution set X represents a convex polyhedral set. In practice, the set X frequently contains degenerate vertices, yielding diverse problems in the determination of an optimal solution as well as in postoptimal analysis.The so called degeneracy graphs represent a useful tool for describing and solving degeneracy problems. The study of degeneracy graphs opens a new field of research with many theoretical aspects and practical applications. The present publication pursues two aims. On the one hand the theory of degeneracy graphs is developed generally, which will serve as a basis for further applications. On the other hand degeneracy graphs will be used to explain simplex cycling, i.e. necessary and sufficient conditions for cycling will be derived.
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