Simplicial Algorithms on the Simplotope

Simplicial Algorithms on the Simplotope

by Timothy M. Doup
     
 

ISBN-10: 0387502335

ISBN-13: 9780387502335

Pub. Date: 10/28/1988

Publisher: Springer-Verlag New York, LLC

This monograph deals with simplicial algorithms on the unit simplex and on the simplotope. Several new triangulations are introduced underlying the simplicial algorithms. The V-triangulation underlies a number of new simplicial algorithms and also underlies a continuous deformation algorithm on the simplotope. The monograph extensively discusses these algorithms

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Overview

This monograph deals with simplicial algorithms on the unit simplex and on the simplotope. Several new triangulations are introduced underlying the simplicial algorithms. The V-triangulation underlies a number of new simplicial algorithms and also underlies a continuous deformation algorithm on the simplotope. The monograph extensively discusses these algorithms and gives computational comparisons. The examples include exchange economies, quadratic programming, non-cooperative N-person games, and economies with a block diagonal supply-demand pattern. In the economic examples, the paths induced by the algorithms can be interpreted as price adjustment processes. These paths have the attractive feature that they always converge to an optimal solution.

Product Details

ISBN-13:
9780387502335
Publisher:
Springer-Verlag New York, LLC
Publication date:
10/28/1988
Series:
Lecture Notes in Economics and Mathemati
Pages:
262
Product dimensions:
9.21(w) x 6.14(h) x 1.16(d)

Table of Contents

I Introduction and Definitions.- 1. Introduction.- 1.1. Introduction.- 1.2. Historical perspective.- 1.3. Outline of the monograph.- 2. Definitions and Existence Theorems.- 2.1. Introduction.- 2.2. Basic concepts and notations.- 2.3. Existence theorems.- 2.4. Labelling functions and accuracy.- 2.5. Pure exchange economies.- 2.6. Quadratically constrained quadratic programming.- 2.7. Economies with a block diagonal supply-demand pattern.- 2.8. Noncooperative N-person games.- 3. Triangulations of Sn and S.- 3.1. Introduction.- 3.2. The Q-triangulation of Sn and S.- 3.3. The Q’-triangulation of S.- 3.4. The V-triangulation of Sn.- 3.5. The V’- and the V-triangulation of S.- 3.6. Variants of the V-triangulation.- II Algorithms on the Unit Simple.- 4. An introduction to Simplicial Algorithms on the Unit Simplex.- 4.1. Introduction.- 4.2. The variable dimension restart algorithm on Sn for proper integer labelling rules.- 4.3. Variable dimension restart algorithms on Sn for arbitrary integer labelling rules.- 4.4. Variable dimension restart algorithms on Sn for vector labelling.- 4.5. A path following interpretation of the variable dimension restart algorithm for the V-triangulation.- 5. The (2n+1-2)-Ray Algorithm.- 5.1. Introduction.- 5.2. The path of the algorithm.- 5.3. The subdivision of Sn.- 5.4. The steps of the algorithm.- 6. The 2-Ray Algorithm.- 6.1. Introduction.- 6.2. The path of the algorithm.- 6.3. The subdivision of Sn.- 6.4. The steps of the algorithm.- 7. Comparisons and Computational Results.- 7.1. Introduction.- 7.2. A comparison of the variable dimension restart algorithms on Sn.- 7.3. Computational results.- III Algorithms on the Simplotope.- 8. An Introduction to Simplicial Algorithms on the Simplotope.- 8.1. Introduction.- 8.2. The sum-ray algorithm on S for proper integer labelling rules.- 8.3. Variable dimension restart algorithms on S for arbitrary integer labelling rules.- 8.4. The sum-ray algorithm on S for vector labelling.- 8.5. A path following interpretation of the sum-ray algorithm for the V’ -triangulation.- 9. The Product-Ray Algorithm.- 9.1. Introduction.- 9.2. The path of the algorithm.- 9.3. The subdivision of S.- 9.4. The steps of the algorithm.- 10. The Exponent-Ray Algorithm.- 10.1. Introduction.- 10.2. The path of the algorithm.- 10.3. The subdivision of S.- 10.4. The steps of the algorithm.- 11. Comparisons and Computational Results.- 11.1. Introduction.- 11.2. A comparison of the variable dimension restart algorithms on S.- 11.3. Computational results.- IV Continuous Deformation on the Simplotope.- 12. The Continuous Deformation Algorithm on the Simplotope.- 12.1. Introduction.- 12.2. The path of the algorithm.- 12.3. Triangulation of S x [1,?).- 12.4. Triangulation of the boundary of S x [1,—).- 12.5. The steps of the continuous deformation algorithm on S.- References.

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