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

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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.

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2024

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Cited by 3 publications

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

Xu,

Li,

et al. 2024

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

Wang,

Lin,

Zhang

et al. 2024

Journal of Mathematics

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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.

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

Zhang,

Lin,

Wang

2024

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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.

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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

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