Global Solver based on the Sperner-Lemma and Mazurkewicz-Knaster-Kuratowski-Lemma based proof of the Brouwer Fixed-Point Theorem
<|reference_start|>Global Solver based on the Sperner-Lemma and Mazurkewicz-Knaster-Kuratowski-Lemma based proof of the Brouwer Fixed-Point Theorem: In this paper a fixed-point solver for mappings from a Simplex into itself that is gradient-free, global and requires $\binom{d+1}{ 2}$ function evaluations for halvening the error is presented. It is based on topological arguments and uses the constructive proof of the Mazurkewicz-Knaster-Kuratowski lemma as used as part of the proof for Brouwers Fixed-Point theorem.<|reference_end|>
@article{moshagen2024global,
    title={Global Solver based on the Sperner-Lemma and
  Mazurkewicz-Knaster-Kuratowski-Lemma based proof of the Brouwer Fixed-Point
  Theorem},
    author={Thilo Moshagen},
    journal={arXiv preprint arXiv:2407.18816},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.18816},
    primaryClass={math.NA cs.NA math.FA}
}