Simplicial fixed point algorithms and applications

Z.F. Yang

Research output: ThesisDoctoral ThesisScientific

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Abstract

Fixed point theory is an important branch of modern mathematics and has always been a major theoretical tool in fields such as differential equations, topology, function analysis, optimal control, economics, and game theory. Its applicability has been increased enormously by the development of simplicial fixed point methods starting in the late 1960s. These methods have become powerful tools for finding solutions to general systems of nonlinear equations, price equilibria, Nash equilibria, core elements, and so on. In this monograph, new simplicial fixed point methods are developed to solve various new fixed point problems to which the existing methods do not apply. The convergence and performance of the methods are thoroughly studied. The theoretical problems considered range from the stability and refinement of stationary points, through the existence of a continuum of fixed points, the existence of equilibria in competitive economies with several indivisible commodities and money, and the existence of equilibria in competitive economies with production, to the feasibility of integer programs and generalizations of the classical Sperner lemma and KKM lemma.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Tilburg University
Supervisors/Advisors
  • Talman, A.J.J., Promotor
Award date12 Jan 1996
Place of PublicationTilburg
Publisher
Print ISBNs9056680080
Publication statusPublished - 1996

Fingerprint

Simplicial Algorithm
Fixed-point Algorithm
Fixed Point Method
Sperner's Lemma
Indivisible
Fixed Point Problem
Fixed Point Theory
System of Nonlinear Equations
Integer Program
Stationary point
Game Theory
Nash Equilibrium
Lemma
Optimal Control
Continuum
Refinement
Branch
Fixed point
Economics
Differential equation

Cite this

Yang, Z. F. (1996). Simplicial fixed point algorithms and applications. Tilburg: CentER, Center for Economic Research.
Yang, Z.F.. / Simplicial fixed point algorithms and applications. Tilburg : CentER, Center for Economic Research, 1996. 249 p.
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Yang, ZF 1996, 'Simplicial fixed point algorithms and applications', Doctor of Philosophy, Tilburg University, Tilburg.

Simplicial fixed point algorithms and applications. / Yang, Z.F.

Tilburg : CentER, Center for Economic Research, 1996. 249 p.

Research output: ThesisDoctoral ThesisScientific

TY - THES

T1 - Simplicial fixed point algorithms and applications

AU - Yang, Z.F.

PY - 1996

Y1 - 1996

N2 - Fixed point theory is an important branch of modern mathematics and has always been a major theoretical tool in fields such as differential equations, topology, function analysis, optimal control, economics, and game theory. Its applicability has been increased enormously by the development of simplicial fixed point methods starting in the late 1960s. These methods have become powerful tools for finding solutions to general systems of nonlinear equations, price equilibria, Nash equilibria, core elements, and so on. In this monograph, new simplicial fixed point methods are developed to solve various new fixed point problems to which the existing methods do not apply. The convergence and performance of the methods are thoroughly studied. The theoretical problems considered range from the stability and refinement of stationary points, through the existence of a continuum of fixed points, the existence of equilibria in competitive economies with several indivisible commodities and money, and the existence of equilibria in competitive economies with production, to the feasibility of integer programs and generalizations of the classical Sperner lemma and KKM lemma.

AB - Fixed point theory is an important branch of modern mathematics and has always been a major theoretical tool in fields such as differential equations, topology, function analysis, optimal control, economics, and game theory. Its applicability has been increased enormously by the development of simplicial fixed point methods starting in the late 1960s. These methods have become powerful tools for finding solutions to general systems of nonlinear equations, price equilibria, Nash equilibria, core elements, and so on. In this monograph, new simplicial fixed point methods are developed to solve various new fixed point problems to which the existing methods do not apply. The convergence and performance of the methods are thoroughly studied. The theoretical problems considered range from the stability and refinement of stationary points, through the existence of a continuum of fixed points, the existence of equilibria in competitive economies with several indivisible commodities and money, and the existence of equilibria in competitive economies with production, to the feasibility of integer programs and generalizations of the classical Sperner lemma and KKM lemma.

M3 - Doctoral Thesis

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T3 - CentER Dissertation Series

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ER -

Yang ZF. Simplicial fixed point algorithms and applications. Tilburg: CentER, Center for Economic Research, 1996. 249 p. (CentER Dissertation Series).