Solving Fixed-Point Problems with Inequality and Equality Constraints via a Non-Interior Point Homotopy Path-Following Method

Abstract EN

In recent years, fixed-point theorems have attracted increasing attention and have been widely investigated by many authors.

Moreover, determining a fixed point has become an interesting topic.

In this paper, we provide a constructive proof of the general Brouwer fixed-point theorem and then obtain the existence of a smooth path which connects a given point to the fixed point.

We also present a non-interior point homotopy algorithm for solving fixed-point problems on a class of nonconvex sets by numerically tricking this homotopy path.