ENGLISH

Degeneracy Graphs and Simplex Cycling

By Peter Zörnig (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1991
ISBN
978-3-540-54593-4, 978-3-642-45702-9
DOI
10.1007/978-3-642-45702-9
Language
english
Format
PDF
Filesize
11 MB (11027694 bytes)
Series
Lecture Notes in Economics and Mathematical Systems 357
Edition
1
Pages
196\210
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Control; Calculus of Variations and Optimal ControOperations Research/Decision Theory; Systems Theor

Description

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 verti- ces, 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 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 of degeneracy graphs is developed generally, which will serve as 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.

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