Complexity bounds for primal-dual methods minimizing the model of objective function

By Yurii E. Nesterov. 2017

117 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Numerical Analysis, Optimization & Training

How researchers see this paper

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

In Artificial Intelligence

1. Simon Lacoste-Julien
2. Martin Jaggi
3. Peter Richtárik
4. Michael I. Jordan
5. Gauthier Gidel
6. Fabian Pedregosa
7. Tianbao Yang
8. Zeyuan Allen-Zhu

In Computational Mechanics

1. Simon Lacoste-Julien
2. Peter Richtárik
3. Martin Jaggi
4. Fabian Pedregosa
5. Michael I. Jordan
6. Gauthier Gidel
7. Tianbao Yang
8. Francis R. Bach

In Numerical Analysis

1. Simon Lacoste-Julien
2. Gauthier Gidel
3. Martin Jaggi
4. Michael I. Jordan
5. Volkan Cevher
6. Fabian Pedregosa
7. Zaïd Harchaoui
8. B. Recht

In Optimization & Training

1. Simon Lacoste-Julien
2. Peter Richtárik
3. Martin Jaggi
4. Gauthier Gidel
5. Fabian Pedregosa
6. Michael I. Jordan
7. Tianbao Yang
8. Jakub Konecný

Citations in the corpus

• Frank-Wolfe Splitting via Augmented Lagrangian Method (2018, background): “Notice that the FW algorithm does not converge if the objective function is not at least continuously differentiable (Nesterov, 2016, Example 1).”
• A Lyapunov Analysis of Momentum Methods in Optimization (2016, methodology): “However, like most implicit discretization techniques applied to the momentum dynamics (4), this does not lead to an algorithm with tractable subproblems.”
• Semi-Proximal Mirror-Prox for Nonsmooth Composite Minimization (2015, methodology): “The composite conditional gradient algorithm was first introduced in [9] and also developed in [21].”
• Linearly Convergent Frank-Wolfe with Backtracking Line-Search. (2018, background): “To the best of our knowledge, primal-dual convergence rates on the last iterate have only been derived in (Nesterov, 2017) and were not extended to approximate linear subproblems nor the Away-steps and Pairwise variants.”
• A Universal Primal-Dual Convex Optimization Framework (2015, methodology): “After our initial draft appeared, [14] presented new GCG-type methods for composite minimization, i.e., min xPR p f pxq`ψpxq, relying on Hölder smoothness of f (i.e., ν P p0, 1s) and the sharp-operator of ψ.”
• Frank-Wolfe Method is Automatically Adaptive to Error Bound Condition (2018, methodology): “In recent years, the FW method has gained an increasing interest in large-scale optimization and machine learning (e.g., (Garber and Hazan, 2015; Freund and Grigas, 2016; Nesterov, 2018; Narasimhan, 2018)).”