Results 21 to 30 of about 1,838,887 (337)

Convergence of inertial dynamics and proximal algorithms governed by maximally monotone operators [PDF]

Mathematical programming, 2017
We study the behavior of the trajectories of a second-order differential equation with vanishing damping, governed by the Yosida regularization of a maximally monotone operator with time-varying index, along with a new Regularized Inertial Proximal ...
H. Attouch, J. Peypouquet
semanticscholar   +1 more source

On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators

Mathematical programming, 1992
This paper shows, by means of an operator called asplitting operator, that the Douglas—Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Therefore, applications of Douglas—
Jonathan Eckstein, D. Bertsekas
semanticscholar   +1 more source

Locally efficient monotone operators [PDF]

Proceedings of the American Mathematical Society, 1990
We study monotone operators on quasi open or convex subsets of a real Banach space X X (quasi open means that the ...
Verona, Andrei, Verona, Maria Elena
openaire   +1 more source

Θ-monotone operators and bifunctions

, 2022
The purpose of this paper is to introduce and investigate θ-monotone operators and θ-monotone bifunctions in the context of Banach space. Local boundedness of θ-monotone bifunctions in the interior of their domains is proved.
Ramazannejad, Maede
core   +1 more source

Weighted modular inequalities for monotone functions

Journal of Inequalities and Applications, 1997
Weight characterizations of weighted modular inequalities for operators on the cone of monotone functions are given in terms of composition operators on arbitrary non-negative functions with changes in weights. The results extend to modular inequalities,
A. Kufner, H. P. Heinig, P. Drábek   +2 more
doaj   +2 more sources

On maximal monotone operators with relatively compact range [PDF]

, 2010
summary:It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator $T$ can be approximated by a sequence ...
Zagrodny, Dariusz
core   +1 more source

ADMM for monotone operators: convergence analysis and rates [PDF]

Advances in Computational Mathematics, 2017
We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces.
R. Boț, E. R. Csetnek
semanticscholar   +1 more source

Newton-like Inertial Dynamics and Proximal Algorithms Governed by Maximally Monotone Operators

SIAM Journal on Optimization, 2020
The introduction of the Hessian damping in the continuous version of Nesterov's accelerated gradient method provides, by temporal discretization, fast proximal gradient algorithms where the oscilla...
H. Attouch, S. László
semanticscholar   +1 more source

Bregman Distance and Strong Convergence of Proximal-Type Algorithms

Abstract and Applied Analysis, 2013
The purpose of this paper is to discuss some fundamental properties of Bregman distance, generalized projection operators, firmly nonexpansive mappings, and resolvent operators of set-valued monotone operators corresponding to a functional Φ(∥·∥).
Li-Wei Kuo, D. R. Sahu
doaj   +1 more source

Forward–backward splitting algorithm for fixed point problems and zeros of the sum of monotone operators

Arabian Journal of Mathematics, 2019
In this paper, we construct a forward–backward splitting algorithm for approximating a zero of the sum of an $$\alpha $$ α -inverse strongly monotone operator and a maximal monotone operator.
V. Dadashi, M. Postolache
semanticscholar   +1 more source