Convergent Dynamics of Nonreciprocal Differential Variational Inequalities Modeling Neural Networks

A new class of differential variational inequalities (DVIs), governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces, is investigated in this paper. More precisely, based on Browder’s result, optimal control theory, measurability of set-valued mappings and the theory of semigroups, we establish that the solution set of DVI is nonempty and compact. In addition, the theoretical developments are accompanied by an application to differential Nash games.

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Existence results of semilinear differential variational inequalities without compactness

Optimization ◽

10.1080/02331934.2019.1571057 ◽

2019 ◽

Vol 68 (5) ◽

pp. 1017-1035 ◽

Cited By ~ 2

Author(s):

Liang Lu ◽

Zhenhai Liu ◽

Dumitru Motreanu

Keyword(s):

Variational Inequalities ◽

Existence Results ◽

Differential Variational Inequalities

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Efficient neural networks for solving variational inequalities

Neurocomputing ◽

10.1016/j.neucom.2012.01.020 ◽

2012 ◽

Vol 86 ◽

pp. 97-106 ◽

Cited By ~ 7

Author(s):

Suoliang Jiang ◽

Deren Han ◽

Xiaoming Yuan

Keyword(s):

Neural Networks ◽

Variational Inequalities

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Formulating and Solving Service Network Pricing and Resource Allocation Games as Differential Variational Inequalities

Annals of the International Society of Dynamic Games - Advances in Dynamic Game Theory ◽

10.1007/978-0-8176-4553-3_29 ◽

2007 ◽

pp. 587-614 ◽

Cited By ~ 3

Author(s):

T. L. Friesz ◽

R. Mookherjee ◽

M. A. Rigdon

Keyword(s):

Resource Allocation ◽

Variational Inequalities ◽

Network Pricing ◽

Service Network ◽

Resource Allocation Games ◽

Differential Variational Inequalities

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Solving complementarity and variational inequalities problems using neural networks

Applied Mathematics and Computation ◽

10.1016/j.amc.2007.01.036 ◽

2007 ◽

Vol 190 (1) ◽

pp. 216-230 ◽

Cited By ~ 9

Author(s):

M. Yashtini ◽

A. Malek

Keyword(s):

Neural Networks ◽

Variational Inequalities

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On output regulation in systems with differential variational inequalities

53rd IEEE Conference on Decision and Control ◽

10.1109/cdc.2014.7039863 ◽

2014 ◽

Cited By ~ 3

Author(s):

Aneel Tanwani ◽

Bernard Brogliato ◽

Christophe Prieur

Keyword(s):

Variational Inequalities ◽

Output Regulation ◽

Differential Variational Inequalities

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A comparison of numerical methods for solving multibody dynamics problems with frictional contact modeled via differential variational inequalities

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2017.03.010 ◽

2017 ◽

Vol 320 ◽

pp. 668-693 ◽

Cited By ~ 11

Author(s):

Daniel Melanz ◽

Luning Fang ◽

Paramsothy Jayakumar ◽

Dan Negrut

Keyword(s):

Numerical Methods ◽

Variational Inequalities ◽

Multibody Dynamics ◽

Frictional Contact ◽

Dynamics Problems ◽

Differential Variational Inequalities

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Decay solutions for a class of fractional differential variational inequalities

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2015-0033 ◽

2015 ◽

Vol 18 (3) ◽

Cited By ~ 1

Author(s):

Tran Dinh Ke ◽

Nguyen Van Loi ◽

Valeri Obukhovskii

Keyword(s):

Fixed Point ◽

Variational Inequalities ◽

Fractional Derivatives ◽

New Class ◽

Fixed Point Approach ◽

Fractional Differential ◽

Differential Variational Inequalities

AbstractOur aim is to study a new class of differential variational inequalities involving fractional derivatives. Using the fixed point approach, the existence of decay solutions to the mentioned problem is proved.

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