An efficient simplicial algorithm for computing a zero of a convex union of smooth functions

DOI10.1007/BF02591720zbMath0493.90074OpenAlexW2010950672MaRDI QIDQ3956756

Michael J. Todd, Samuel A. Awoniyi

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1007/bf02591720

zbMATH Keywords

computational experimentseconomic equilibriumQ-superlinear convergencecomputation of a zeroconvex union of smooth functionsefficient simplicial algorithmNullstellepiecewise-linear homotopypoint- to-set mapping

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Applications of mathematical programming (90C90) Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Mathematical economics (91B99) General equilibrium theory (91B50)

Related Items

$J'$: A New Triangulation of $R^n $, Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications

Uses Software

• PLALGO

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on computing equilibria in economies with activity analysis models of production
• The computation of fixed points and applications
• A quadratically-convergent fixed-point algorithm for economic equilibria and linearly constrained optimization
• Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
• An Index Theorem for General Equilibrium Models with Production
• Traversing Large Pieces of Linearity in Algorithms that Solve Equations by Following Piecewise-Linear Paths
• A class of simplicial restart fixed point algorithms without an extra dimension
• A simplicial algorithm for the nonlinear complementarity problem
• On the Convergence Rate of Algorithms for Solving Equations that are Based on Methods of Complementary Pivoting
• On the homotopic approach to systems of equations with separable mappings
• Improving the convergence of fixed-point algorithms
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• The Approximation of Fixed Points of a Continuous Mapping
• Some theorems on the core of ann-Game without Side-Payments