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.
Contents: Introduction.- Definitions and Existence Theorems. Triangulations of Sn and S.- Algorithms on the Unit Simplex: An Introduction to Simplicial Algorithms on the Unit Simplex. The (2n+1-2)-Ray Algorithm. The 2-Ray Algorithm. Comparisons and Computational Results.- Algorithms on the Simplotope: An Introduction to Simplicial Algorithms on the Simplotope. The Product-Ray Algorithm. The Exponent-Ray Algorithm. Comparisons and Computational Results.- Continuous Deformation on the Simplotope: The Continuos Deformation Algorithm on the Simplotope.- References.
Series: Lecture Notes in Economic and Mathematical Systems
Number Of Pages: 262
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6
Weight (kg): 0.39