Global solver based on the Sperner lemma and Mazurkewicz–Knaster‐Kuratowski–lemma based proof of the Brouwer fixed‐point theorem
Abstract
Abstract In this paper a fixed‐point solver for mappings from a simplex into itself that is gradient‐free, global and requires function evaluations for halving the error is presented, where is the dimension. It is based on topological arguments and uses the constructive proof of the Mazurkewicz–Knaster–Kuratowski lemma when used as part of the proof for Brouwer's fixed‐point theorem.
Fields of Study & Subjects
Fixed Point Theorems Analysis
Iterative Methods for Nonlinear Equations
Optimization and Variational Analysis
Publication details
- Journal / source
- ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
- Volume
- 106
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN