A Neural Network Based on the Metric Projector for Solving SOCCVI Problem

Juhe Sun, Weichen Fu, Jan Harold Alcantara, Jein Shan Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We propose an efficient neural network for solving the second-order cone constrained variational inequality (SOCCVI). The network is constructed using the Karush-Kuhn-Tucker (KKT) conditions of the variational inequality (VI), which is used to recast the SOCCVI as a system of equations by using a smoothing function for the metric projection mapping to deal with the complementarity condition. Aside from standard stability results, we explore second-order sufficient conditions to obtain exponential stability. Especially, we prove the nonsingularity of the Jacobian of the KKT system based on the second-order sufficient condition and constraint nondegeneracy. Finally, we present some numerical experiments, illustrating the efficiency of the neural network in solving SOCCVI problems. Our numerical simulations reveal that, in general, the new neural network is more dominant than all other neural networks in the SOCCVI literature in terms of stability and convergence rates of trajectories to SOCCVI solution.

Original languageEnglish
Article number9159914
Pages (from-to)2886-2900
Number of pages15
JournalIEEE Transactions on Neural Networks and Learning Systems
Volume32
Issue number7
DOIs
Publication statusPublished - 2021 Jul

Keywords

  • Metric projector
  • neural network
  • second-order cone (SOC)
  • second-order sufficient condition
  • stability
  • variational inequality (VI)

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence

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