Solving Fixed-Point Problems with Inequality and Equality Constraints via a Non-Interior Point Homotopy Path-Following Method
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2017-01-01
|
| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2017/3456834 |
| Summary: | 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. |
|---|---|
| ISSN: | 1024-123X 1563-5147 |