Forward–Backward–Half Forward Dynamical Systems for Monotone Inclusion Problems with Application to v-GNE

2021 ◽  
Author(s):  
Pankaj Gautam ◽  
Daya Ram Sahu ◽  
Avinash Dixit ◽  
Tanmoy Som
Keyword(s):  
Dynamical Systems ◽  
Monotone Inclusion ◽  
Inclusion Problems

scholarly journals Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure

2020 ◽  
Vol 10 (1) ◽  
pp. 450-476
Author(s):  
Radu Ioan Boţ ◽  
Sorin-Mihai Grad ◽  
Dennis Meier ◽  
Mathias Staudigl
Keyword(s):  
Dynamical Systems ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Monotone Operators ◽  
Inclusion Problem ◽  
Minimum Norm ◽  
Monotone Inclusion ◽  
Inclusion Problems ◽  
Monotone Inclusion Problem ◽  
Maximally Monotone Operators

Abstract In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of trajectories towards the minimum norm solution of the underlying monotone inclusion problem. To that end, we investigate in detail the asymptotic behavior of dynamical systems perturbed by a Tikhonov regularization where either the maximally monotone operators themselves, or the vector field of the dynamical system is regularized. In both cases we prove strong convergence of the trajectories towards minimum norm solutions to an underlying monotone inclusion problem, and we illustrate numerically qualitative differences between these two complementary regularization strategies. The so-constructed dynamical systems are either of Krasnoselskiĭ-Mann, of forward-backward type or of forward-backward-forward type, and with the help of injected regularization we demonstrate seminal results on the strong convergence of Hilbert space valued evolutions designed to solve monotone inclusion and equilibrium problems.

scholarly journals Second Order Forward-Backward Dynamical Systems For Monotone Inclusion Problems

2016 ◽  
Vol 54 (3) ◽  
pp. 1423-1443 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek
Keyword(s):  
Dynamical Systems ◽  
Second Order ◽  
Monotone Inclusion ◽  
Inclusion Problems

A New Algorithm for Monotone Inclusion Problems and Fixed Points on Hadamard Manifolds with Applications

2021 ◽  
Vol 41 (4) ◽  
pp. 1250-1262
Author(s):  
Shih-sen Chang ◽  
Jinfang Tang ◽  
Chingfeng Wen
Keyword(s):  
Fixed Points ◽  
Hadamard Manifolds ◽  
Monotone Inclusion ◽  
Inclusion Problems

scholarly journals Inertial Douglas–Rachford splitting for monotone inclusion problems

2015 ◽  
Vol 256 ◽  
pp. 472-487 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek ◽  
Christopher Hendrich
Keyword(s):  
Monotone Inclusion ◽  
Inclusion Problems

scholarly journals An Approximate Proximal Point Algorithm for Maximal Monotone Inclusion Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Lingling Huang ◽  
Sanyang Liu ◽  
Weifeng Gao
Keyword(s):  
Hilbert Spaces ◽  
Proximal Point Algorithm ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Computational Results ◽  
Monotone Inclusion ◽  
Proximal Point ◽  
Inclusion Problems ◽  
Correction Step

This paper presents and analyzes a strongly convergent approximate proximal point algorithm for finding zeros of maximal monotone operators in Hilbert spaces. The proposed method combines the proximal subproblem with a more general correction step which takes advantage of more information on the existing iterations. As applications, convex programming problems and generalized variational inequalities are considered. Some preliminary computational results are reported.

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