A practical approach to optimization

TL;DR

This paper introduces a practical optimization method for continuous functions that bypasses traditional conditions, enabling the computation of Brouwer fixed points without complex verification steps.

Contribution

It proposes a novel approach for optimization that avoids Lagrange and KKT conditions, simplifying the process of finding fixed points in continuous functions.

Findings

Successfully finds minimal values of arbitrary continuous functions.

Enables computation of Brouwer fixed points without traditional verification.

Simplifies the optimization process for continuous functions.

Abstract

We present a new approach for finding a minimal value of an arbitrary function assuming only its continuity. The process avoids verifying Lagrange- or KKT-conditions. The method enables us to obtain a Brouwer fixed point (of a continuous function mapping from a cube into itself).