Buch, Englisch, 196 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 382 g
Buch, Englisch, 196 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 382 g
Reihe: Lecture Notes in Economics and Mathematical Systems
ISBN: 978-3-540-54593-4
Verlag: Springer
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
1. Introduction.- 2. Degeneracy problems in mathematical optimization.- 2.1. Convergence problems in the case of degeneracy.- 2.2 Efficiency problems in the case of degeneracy.- 2.3 Degeneracy problems within the framework of postoptimal analysis.- 2.4. On the practical meaning of degeneracy.- 3. Theory of degeneracy graphs.- 3.1. Fundamentals.- 3.2 Theory of ? × n-degeneracy graphs.- 3.3. Theory of 2 × n-degeneracy graphs.- 4. Concepts to explain simplex cycling.- 4.1. Specification of the question.- 4.2 A pure graph theoretical approach.- 4.3 Geometrically motivated approaches.- 4.4 A determinant approach.- 5. Procedures for constructing cycling examples.- 5.1 On the practical use of constructed cycling examples.- 5.2 Successive procedures for constructing cycling examples.- 5.3 On the construction of general cycling examples.- A. Foundations of linear algebra and the theory of convex polytopes.- B. Foundations of graph theory.- C. Problems in the solution of determinant inequality systems.- References.
