Finite time convergent recurrent neural network for variational inequality problems subject to equality constraints

Conchas, Robin F.; Loukianov, Alexander G.; Sanchez, Edgar N.; Alanis, Alma Y.

doi:10.1016/j.jfranklin.2023.11.041

Journal of the Franklin Institute

2024

DOI: 10.1016/j.jfranklin.2023.11.041

|View full text |Cite

Finite time convergent recurrent neural network for variational inequality problems subject to equality constraints

Robin F. Conchas,

Alexander G. Loukianov,

Edgar N. Sanchez

et al.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Impulsive Projection Neural Networks for Variational Inequalities and Sparse Signal Reconstruction Application

Xu,

Li,

et al. 2024

Cogn Comput

View full text Add to dashboard Cite

Impulsive Projection Neural Networks for Variational Inequalities and Sparse Signal Reconstruction Application

Xu,

Li,

et al. 2024

Cogn Comput

View full text Add to dashboard Cite

A Neural Network Based on a Nonsmooth Equation for a Box Constrained Variational Inequality Problem

Wang,

Lin,

Zhang

et al. 2024

Journal of Mathematics

View full text Add to dashboard Cite

The variational inequality framework holds significant prominence across various domains including economic finance, network transportation, and game theory. In addition, a novel approach utilizing a neural network model is introduced in the current work to address a box constrained variational inequality problem. Initially, the original problem is reformulated into a nonsmooth equation, following which the neural network model is meticulously devised to tackle this reformulated equation. This study comprehensively investigated inherent characteristics and properties of this neural network model. In addition, employing the Lyapunov function method, stability analysis of the neural network model proposed is rigorously demonstrated in the Lyapunov sense. Furthermore, the efficacy of the proposed technique is substantiated through numerical simulations, providing empirical support for its applicability and effectiveness.

show abstract

Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets

Zhang,

Lin,

Wang

2024

Axioms

View full text Add to dashboard Cite

Distributionally robust optimization (DRO) is an advanced framework within the realm of optimization theory that addresses scenarios where the underlying probability distribution governing the data is uncertain or ambiguous. In this paper, we introduce a novel class of DRO challenges where the probability distribution of random variables is contingent upon the decision variables, and the ambiguity set is defined through parameterization involving the mean and a covariance matrix, which also depend on the decision variables. This dependency makes DRO difficult to solve directly; therefore, first, we demonstrate that under the condition of a full-space support set, the original problem can be reduced to a second-order cone programming (SOCP) problem. Subsequently, we solve this second-order cone programming problem using a projection differential equation approach. Compared with the traditional methods, the differential equation method offers advantages in providing continuous and smooth solutions, offering inherent stability analysis, and possessing a rich mathematical toolbox, which make the differential equation a powerful and versatile tool for addressing complex optimization challenges.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Finite time convergent recurrent neural network for variational inequality problems subject to equality constraints

Cited by 3 publications

References 25 publications

Impulsive Projection Neural Networks for Variational Inequalities and Sparse Signal Reconstruction Application

Impulsive Projection Neural Networks for Variational Inequalities and Sparse Signal Reconstruction Application

A Neural Network Based on a Nonsmooth Equation for a Box Constrained Variational Inequality Problem

Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets

Contact Info

Product

Resources

About