A simple algorithm for a class of nonsmooth convex-concave saddle-point problems

By Yoel Drori, Shoham Sabach, Marc Teboulle. 2015

108 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Numerical Analysis

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. Peter Richtárik
2. Ming Yan
3. Laurent Condat
4. Ahmed Khaled
5. Thomas Pock
6. Dmitry Kovalev
7. Konstantin Mishchenko
8. Adil Salim

In Mathematical Physics

1. Laurent Condat
2. Ming Yan
3. Antonin Chambolle
4. Thomas Pock
5. Peter Richtárik
6. Adil Salim
7. Konstantin Mishchenko
8. Akira Hirabayashi

In Numerical Analysis

1. Peter Richtárik
2. Ming Yan
3. Thomas Pock
4. Adil Salim
5. Antonin Chambolle
6. Ahmed Khaled
7. Zhi Li
8. Konstantin Mishchenko

Citations in the corpus

• Distributed Fixed Point Methods with Compressed Iterates (2019, background): “The PAPC algorithm [10,17,32] is an algorithm for minimizing F + H ◦ L , where F is smooth and convex, H is nonsmooth and convex and L is a linear operator.”
• Proximal Splitting Algorithms: A Tour of Recent Advances, with New Twists. (2020, methodology): “It was then rediscovered several times and named Primal–Dual Fixed-Point algorithm based on the Proximity Operator (PDFP2O) [50] or Proximal Alternating Predictor–Corrector (PAPC) algorithm [51].”
• A primal-dual algorithm with optimal stepsizes and its application in decentralized consensus optimization (2017, methodology): “:3) l degenerates to h , and the problem (1) becomes It is equivalent to the following saddle-point problem In order to solve (2) (or (3)), a primal-dual algorithm was proposed in different fields under different names [5,9,16].”
• Variance Reduction for Matrix Games (2019, background): “In recent years, minimax formulations for neural network training rose to prominence [15, 23], leading to intense interest in algorithms for solving large scale minimax games [10, 14, 20, 9, 18, 24].”
• On the ergodic convergence rates of a first-order primal–dual algorithm (2016, result): “Also, a very recent work of Drori, Sabach and Teboulle, establishes similar results on a closely related primal-dual (“PAPC”) algorithm [11], which also handles explicit terms, but cannot jointly handle (without further splitting) nonsmooth functions in both the primal and dual variables.”
• Distributed Proximal Splitting Algorithms with Rates and Acceleration (2020, methodology): “IfR = 0, the PD3O and PDDY algorithms revert to the Loris–Verhoeven algorithm [17], also discovered independently as the PDFP2O [6] and PAPC [13] algorithms; see also [9, 10] for an analysis as a primal-dual forward-backward algorithm.”
• Dualize, Split, Randomize: Fast Nonsmooth Optimization Algorithms (2020, methodology): “In the deterministic case gk+1 = ∇F (xk), LiCoSGD reverts to an instance of the algorithm first proposed by Loris and Verhoeven in [52], and rediscovered independently as the PDFP2O algorithm [15] and the Proximal Alternating Predictor-Corrector (PAPC) algorithm [30].”