Excellence in Research and Innovation for Humanity

Shaoyun Shi

Publications

1

Publications

1
11175
A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets
Abstract:

In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

Keywords:
interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm