Fast gradient descent method for convex optimization problems with an oracle that generates a $(\delta,L)$-model of a function in a requested point

Alexander Gasnikov; Alexander Tyurin

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Fast gradient descent method for convex optimization problems with an oracle that generates a $(\delta,L)$-model of a function in a requested point

Alexander Tyurin, Alexander Gasnikov

Optimization and Control · Submitted 7 Nov 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using this concept we describe the gradient descent method and the fast gradient descent method and we show that many popular methods (composite optimization methods, level methods, conjugate gradient methods, proximal methods) are special cases of proposed methods in this article.

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arXiv ID1711.02747 (version 5)

Pith IDIQ57DBBK, Pith's permanent record of this paper and its review

CitationAlexander Gasnikov, Alexander Tyurin. "Fast gradient descent method for convex optimization problems with an oracle that generates a $(\delta,L)$-model of a function in a requested point." arXiv:1711.02747 (2017). https://pith.science/paper/IQ57DBBK

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In this article we propose a new concept of a $(\delta,L)$-model of a function which generalizes the concept of the $(\delta,L)$-oracle (Devolder-Glineur-Nesterov). Using this concept we describe the gradient descent method and the fast gradient descent method and we show that many popular methods (composite optimization methods, level methods, conjugate gradient methods, proximal methods) are special cases of proposed methods in this article.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this article we propose a new concept of a $(\delta,L)$-model of a function which generalizes the concept of the $(\delta,L)$-oracle (Devolder-Glineur-Nesterov).	contribution 1.00	0.88	0.16	asserted 1.00
s1	Using this concept we describe the gradient descent method and the fast gradient descent method and we show that many popular methods (composite optimization methods, level methods, conjugate gradient methods, proximal methods) are special cases of proposed methods in this article.	contribution 0.85	0.92	0.57	asserted 1.00

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Original abstract

In this article we propose a new concept of a $(\delta,L)$-model of a function which generalizes the concept of the $(\delta,L)$-oracle (Devolder-Glineur-Nesterov). Using this concept we describe the gradient descent method and the fast gradient descent method and we show that many popular methods (composite optimization methods, level methods, conjugate gradient methods, proximal methods) are special cases of proposed methods in this article.

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5 arXiv papers cite this in 12 sentences

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Next we define the inexact model of the objective function, which generalizes the inexact oracle of [ref] (see also [ref] ).

Gradient Methods for Problems with Inexact Model of the Objective · Gradient Methods with Inexact Model of the Objective · 0.91

Uses its method or tool 1 paper

But we include in the survey the description of the Universal Accelerated Gradient Descent algorithm [ref] which in the general case can also be applied to a wide variety of problems.

Advances in Low-Memory Subgradient Optimization · Concluding remarks · 0.80

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Some adaptive proximal method for a special class of variational inequalities and related problems · �� · 0.95

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