Overview

Many problems in economics can be formulated as early 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. 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 monograph pursues two aims. On the one hand, the theory of degeneracy graphs is developed generally, to serve as a basis for further applications. On the other hand, degeneracy graphs are used to explain simplex cycling, and necessary and sufficient conditions for cycling are derived.

Full Product Details

Author:   Peter Zörnig
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1991
Volume:   357
Dimensions:   Width: 17.00cm , Height: 1.10cm , Length: 24.40cm
Weight:   0.382kg
ISBN:  

9783540545934

ISBN 10:   354054593
Pages:   196
Publication Date:   13 November 1991
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

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.

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