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

Autor: Radu Ioan Bot, Mathias Staudigl, Dennis Meier, Sorin-Mihai Grad

Publikováno v: Advances in Nonlinear Analysis, Vol 10, Iss 1, Pp 450-476 (2020)
Advances in Nonlinear Analysis
Advances in Nonlinear Analysis, De Gruyter, 2021, 10 (1), pp.450-476. ⟨10.1515/anona-2020-0143⟩
Advances in Nonlinear Analysis, 10(1), 450-476. De Gruyter

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

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f826ec1795a6b7397d427eeab53203b8
https://doaj.org/article/956c2fa00fca4524a8984672ca1a0b3c

A strongly convergent Krasnosel’skiǐ–Mann-type algorithm for finding a common fixed point of a countably infinite family of nonexpansive operators in Hilbert spaces

Autor: Dennis Meier, Radu Ioan Bot

Publikováno v: Journal of Computational and Applied Mathematics. 395:113589

In this article, we propose a Krasnosel’skiǐ–Mann-type algorithm for finding a common fixed point of a countably infinite family of nonexpansive operators ( T n ) n ≥ 0 in Hilbert spaces. We formulate an asymptotic property which the family (

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::348f6f41b4579dd75415cee6a8a61df1
https://doi.org/10.1016/j.cam.2021.113589

Second Order Forward-Backward Dynamical Systems For Monotone Inclusion Problems

Autor: Radu Ioan Bot, Ernö Robert Csetnek

Publikováno v: SIAM Journal on Control and Optimization. 54:1423-1443

We begin by considering second order dynamical systems of the from $\ddot x(t) + \gamma(t)\dot x(t) + \lambda(t)B(x(t))=0$, where $B: {\cal H}\rightarrow{\cal H}$ is a cocoercive operator defined on a real Hilbert space ${\cal H}$, $\lambda:[0,+\inft

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::86f7959b5c99fc7bdb09d7f15b7131f6
https://doi.org/10.1137/15m1012657

A variable smoothing algorithm for solving convex optimization problems

Autor: Radu Ioan Bot, Christopher Hendrich

Publikováno v: TOP. 23:124-150

In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the latter to a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0718e1002f5a539b3f932818825f9d05
https://doi.org/10.1007/s11750-014-0326-z

THE IMPACT OF A CURIOUS TYPE OF SMOOTHNESS CONDITIONS ON CONVERGENCE RATES IN l^1 -REGULARIZATION

Autor: Radu Ioan Bot, Bernd Hofmann

Publikováno v: Eurasian Journal of Mathematical and Computer Applications. 1:29-40

Tikhonov-type regularization of linear and nonlinear ill-posed problems in abstract spaces under sparsity constraints gained relevant attention in the past years. Since under some weak assumptions all regularized solutions are sparse if the ‘ 1 -no

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::011cfa2b0efb2d31d859f6fb50b7311f
https://doi.org/10.32523/2306-3172-2013-1-1-29-40