A new class of neural networks for NCPs using smooth perturbations of the natural residual function

Jan Harold Alcantara, Jein Shan Chen*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

摘要

We present a new class of neural networks for solving nonlinear complementarity problems (NCPs) based on some family of real-valued functions (denoted by ℱ) that can be used to construct smooth perturbations of the level curve defined by ΦNR(x,y)=0, where ΦNR is the natural residual function (also called the “min” function). We introduce two important subclasses of ℱ, which deserve particular attention because of their significantly different theoretical and numerical properties. One of these subfamilies yields a smoothing function for ΦNR, while the other subfamily only yields a smoothing curve for ΦNR(x,y)=0. We also propose a simple framework for generating functions from these subclasses. Using the smoothing approach, we build two types of neural networks and provide sufficient conditions to guarantee asymptotic and exponential stability of equilibrium solutions. Finally, we present extensive numerical experiments to validate the theoretical results and to illustrate the difference in numerical performance of functions from the two subclasses. Numerical comparisons with existing neural networks for NCPs are also demonstrated.

原文英語
文章編號114092
期刊Journal of Computational and Applied Mathematics
407
DOIs
出版狀態已發佈 - 2022 6月

ASJC Scopus subject areas

  • 計算數學
  • 應用數學

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