Universal gradient methods for convex optimization problems

By Yurii E. Nesterov. Mathematical programming, 2015

401 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/98ef3a4762fada3820a13c4f4786165bd6c15760

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

In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Online Adaptive Methods, Universality and Acceleration (2018, methodology): “Conversely, the universal gradient methods presented in [25] rely on a line search procedure, which requires exact gradients and function values, and are therefore inappropriate for stochastic optimization.”
An Optimal Affine Invariant Smooth Minimization Algorithm (2013, methodology): “e now prove a simple Lemma controlling the smoothness of f terms of k · kp. This idea is a minor extension of the “inexact gradient trick” proposed in [ Devolder et al., 2011] and further studied in [Nesterov, 2015], which corresponds to the special case where p = 2 in the results described here. As”
On lower complexity bounds for large-scale smooth convex optimization (2013, background): “It should be mentioned that for the case 2 ≤ p < ∞ the lower bounds in this paper were announced in [13, 14] (and proved by the second author of this paper); however, aside of the very special case of p = 2, the highly technical original proofs of the bounds were never published.”
A Universal Primal-Dual Convex Optimization Framework (2015, methodology): “For the accelerated variant, we study an alternative to the universal accelerated method of [15] based on FISTA [10] since it requires less proximal operators in the dual.”
An introduction to continuous optimization for imaging (2016, background): “It is also possible to derive accelerated schemes for problems with different types of smoothness (such as Hölder-continuous gradients); see Nesterov (2015).”
Convex Optimization for Big Data: Scalable, randomized, and parallel algorithms for big data analytics (2014, methodology): “7PGM in [48] uses the Bregman / prox setup.”
Complexity bounds for primal-dual methods minimizing the model of objective function (2017, methodology): “In this sense, method (2.9) is a universal method for solving the problem (2.1) (see [16]).”
Stochastic model-based minimization of weakly convex functions (2018, methodology): “The observation that Algorithm 1.2 is an approximate descent method on the Moreau envelope (1.3) is tangentially related to the recent work on “inexact ﬁrst-order oracles” in convex optimization [25,48] and its partial extensions to nonconvex settings [33].”
Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent (2014, neutral): “Although accelerated gradient methods have been widely applied (to mention a few, see [38, 39] for regularized optimizations, [19, 30] for composite optimization, [29] for cubic regularization, [31] for universal method, and [20] for an application on maxflow), they are often regarded as “analytical”
Optimal Affine-Invariant Smooth Minimization Algorithms (2018, methodology): “We now briefly illustrate the numerical performance of our methods on a simple problem taken from Nesterov (2015).”
A Dual Approach for Optimal Algorithms in Distributed Optimization over Networks (2018, neutral): “see [62] (Lemma 1), [25] (Lemma 1) and [59] (Theorem 1).”
Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization (2020, methodology): “, The ideas used in the proof can be found in the proofs of [17, Lemma 5.7], [40 Lemma 2], and in [18, Section 2.3].”