A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings

By Paul Tseng. SIAM Journal of Control and Optimization, 2000

461 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3362f504c066888b4241a5b6bdaf919783a9ac9f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Radu Ioan Bot
2. Ernö Robert Csetnek
3. Yekini Shehu

In Computational Theory and Mathematics

1. Ernö Robert Csetnek
2. Radu Ioan Bot
3. Yekini Shehu

In Numerical Analysis

1. Ernö Robert Csetnek
2. Radu Ioan Bot

Citations in the corpus

• A Hybrid Proximal-Extragradient Algorithm with Inertial Effects (2014, unknown): “Let us notice that the forward-backward and the forward-backward-forward (see [28]) algorithms are designed to find the zeros of the sum of two maximally monotone operators, one of them being single-valued, their formulations depending whether the single-valued operator is cocoercive or (only) monot”
• Forward-Backward and Tseng’s Type Penalty Schemes for Monotone Inclusion Problems (2013, methodology): “The iterative method we propose in this setting is a forward-backward-forward penalty scheme and relies on a method introduced by Tseng in [23] (see [4, 12, 15] for further details and motivations).”
• An inertial forward–backward splitting method for solving inclusion problems in Hilbert spaces (2018, unknown): “1), the forward–backward splitting method [11,18,28,29,33,41] is usually employed and is defined by the following manner: x1 ∈ H and xn+1 = (I + rB)−1(xn − rAxn), n ≥ 1, (1.”
• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers (2011, unknown): “Other representative publications include [62, 143, 59, 147, 158, 159, 42].”
• A Generalized Forward-Backward Splitting (2011, unknown): “This algorithm, which finds its roots in numerical analysis for PDEs, has been well studied for solving monotone inclusion and convex optimization problems [9, 19, 27, 45, 57, 62, 73, 75].”
• ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems and GANs (2019, unknown): “[65] P.”