This article is cited in 19 papers

Fast gradient descent for convex minimization problems with an oracle producing a $(\delta,L)$-model of function at the requested point

A. V. Gasnikov^abc, A. I. Turin<sup>a

a</sup> State University – Higher School of Economics, Moscow, 125319 Russia
^b Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141700 Russia
^c Kharkevich Institute for Information Transmission Problems, Moscow, 127051 Russia

Abstract: A new concept of $(\delta,L)$ -model of a function that is a generalization of the Devolder–Glineur–Nesterov $(\delta,L)$-oracle is proposed. Within this concept, the gradient descent and fast gradient descent methods are constructed and it is shown that constructs of many known methods (composite methods, level methods, conditional gradient and proximal methods) are particular cases of the methods proposed in this paper.

Key words: gradient descent, fast gradient descent, model of function, universal method, conditional gradient method, composite optimization.

UDC: 519.85

Received: 08.11.2017
Revised: 08.11.2017
Accepted: 11.03.2019

DOI: 10.1134/S0044466919070081

 English version: Computational Mathematics and Mathematical Physics, 2019, 59:7, 1085–1097

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