Degeneracy Graphs and Simplex Cycling

by Peter Zörnig

Many problems in economics can be formulated as linearlyconstrained mathematical optimization problems, where thefeasible solution set X represents a convex polyhedral set.In practice, the set X frequently contains degenerate verti-ces, yielding diverse problems in the determination of anoptimal solution as well as in postoptimal analysis.The so-called degeneracy graphs represent a useful tool for des-cribing and solving degeneracy problems. The study of dege-neracy graphs opens a new field of research with many theo-retical aspects and practical applications. The present pu-blication pursues two aims. On the one hand the theory ofdegeneracy graphs is developed generally, which will serveas a basis for further applications. On the other hand dege-neracy graphs will be used to explain simplex cycling, i.e.necessary and sufficient conditions for cycling will be de-rived.

212 pages, Paperback

First published December 1, 1991