A new variable dimension algorithm for the fixed point problem

DOI10.1007/BF02594783zbMath0495.90071MaRDI QIDQ3959753

Yoshitsugu Yamamoto

Publication date: 1983

Published in: Mathematical Programming (Search for Journal in Brave)

zbMATH Keywords

system of nonlinear equationsfixed pointsequence of subproblemspiecewise linear equationsvariable dimension algorithm

Mathematics Subject Classification ID

Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10) Fixed-point and coincidence theorems (topological aspects) (54H25)

Related Items (13)

A variable-dimension homotopy on networks for computing linear spatial equilibria ⋮ A simplicial homotopy algorithm for computing zero points on polytopes ⋮ A better triangulation for Wright's \(2^n\)-ray algorithm ⋮ Simplicial approximation of solutions to the nonlinear complementarity problem with lower and upper bounds ⋮ A unifying model based on retraction for fixed point algorithms ⋮ Computational complexity of a piecewise linear homotopy algorithm ⋮ A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm ⋮ Computing an integer point of a class of convex sets. ⋮ Computing an integer point of a simplex with an arbitrary starting homotopy-like simplicial algorithm ⋮ Solving discrete zero point problems ⋮ Efficiency and implementation of simplicial zero point algorithms ⋮ Simplicial zero-point algorithms: A unifying description ⋮ A variable dimension fixed point algorithm and the orientation of simplices

Cites Work

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• The computation of fixed points and applications
• Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
• A class of simplicial restart fixed point algorithms without an extra dimension
• A variable dimension algorithm for the linear complementarity problem
• A variable-dimension simplicial algorithm for antipodal fixed-point theorems
• The Solution of Systems of Piecewise Linear Equations
• The octahedral algorithm, a new simplicial fixed point algorithm
• A Modified Integer Labeling for Complementarity Algorithms
• A restart algorithm for computing fixed points without an extra dimension
• Variable dimension algorithms: Basic theory, interpretations and extensions of some existing methods

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