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

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  • Menglong Su
  • Yufeng Shang

Abstract

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.

Suggested Citation

  • Menglong Su & Yufeng Shang, 2017. "Solving Fixed-Point Problems with Inequality and Equality Constraints via a Non-Interior Point Homotopy Path-Following Method," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-9, November.
    • Handle: RePEc:hin:jnlmpe:3456834
    DOI: 10.1155/2017/3456834
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