Results 21 to 30 of about 30,811 (272)

Generalized Forward-Backward Splitting with Penalization for Monotone Inclusion Problems

, 2014
We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another ...
Andrea Porras-Alfaro (3275619), Emily C. Farrer (2926542), Katharine N. Suding (331341), Robert L. Sinsabaugh (2905805), Sarah L. Dean (3275622)   +4 more
core   +3 more sources

Homogenization of multivalued monotone operators with variable growth exponent

Networks and Heterogeneous Media, 2020
We consider the Dirichlet problem for an elliptic multivalued maximal monotone operator $ {\mathcal A}_\varepsilon $ satisfying growth estimates of power type with a variable exponent.
Svetlana Pastukhova, Valeria Chiadò Piat   +1 more
doaj   +1 more source

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

, 2010
In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions.
A. Moudafi, A. Moudafi, C. Zăalinescu, C. Zălinescu, H. Attouch, H. Attouch, J.-E. Martínez-Legaz, J.M. Borwein, M. Marques Alves, R.I. Boţ, R.I. Boţ, R.I. Boţ, R.T. Rockafellar, Radu Ioan Boţ, S. Bartz, S. Simons, Sorin-Mihai Grad   +16 more
core   +1 more source

Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators

Journal of Inequalities and Applications, 2017
In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods.
Tadchai Yuying, Somyot Plubtieng
doaj   +1 more source

A measure differential inclusion involving time-dependent maximal\n monotone operators [PDF]

, 2021
Dalila Azzam-Laouir
openalex   +2 more sources

Iterative Algorithms for New General Systems of Set-Valued Variational Inclusions Involving (A,η)-Maximal Relaxed Monotone Operators

Journal of Applied Mathematics, 2014
We introduce and study a class of new general systems of set-valued variational inclusions involving (A,η)-maximal relaxed monotone operators in Hilbert spaces.
Ting-jian Xiong, Heng-you Lan
doaj   +1 more source

Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator

, 2012
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of $A+
Borwein, Jonathan M., Yao, Liangjin
core   +1 more source

Stochastic homogenization of maximal monotone relations and applications

Networks and Heterogeneous Media, 2018
We study the homogenization of a stationary random maximal monotone operator on a probability space equipped with an ergodic dynamical system. The proof relies on Fitzpatrick's variational formulation of monotone relations, on Visintin's scale ...
Luca Lussardi, Stefano Marini, Marco Veneroni   +2 more
doaj   +1 more source

Monotone Riemannian Metrics and Relative Entropy on Non-Commutative Probability Spaces

, 1998
We use the relative modular operator to define a generalized relative entropy for any convex operator function g on the positive real line satisfying g(1) = 0.
Lesniewski, Andrew, Ruskai, Mary Beth
core   +1 more source

Detecting homologous recombination deficiency for breast cancer through integrative analysis of genomic data

Molecular Oncology, EarlyView.
This study develops a semi‐supervised classifier integrating multi‐genomic data (1404 training/5893 validation samples) to improve homologous recombination deficiency (HRD) detection in breast cancer. Our method demonstrates prognostic value and predicts chemotherapy/PARP inhibitor sensitivity in HRD+ tumours.
Rong Zhu, Katherine Eason, Suet‐Feung Chin, Paul A. W. Edwards, Raquel Manzano Garcia, Richard Moulange, Jia Wern Pan, Soo Hwang Teo, Sach Mukherjee, Maurizio Callari, Carlos Caldas, Stephen‐John Sammut, Oscar M. Rueda   +12 more
wiley   +1 more source