Adaptive Gradient Methods for Some Classes of Non-Smooth Optimization Problems

Fedor Stonyakin

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arXiv · 1911.08425

Adaptive Gradient Methods for Some Classes of Non-Smooth Optimization Problems

Fedor Stonyakin

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Abstract

We propose several adaptive algorithmic methods for problems of non-smooth convex optimization. The first of them is based on a special artificial inexactness. Namely, the concept of inexact ($ \delta, \Delta, L$)-model of objective functional in optimization is introduced and some gradient-type methods with adaptation of inexactness parameters are proposed. A similar concept of an inexact model is introduced for variational inequalities as well as for saddle point problems. Analogues of switching sub-gradient schemes are proposed for convex programming problems with some general assumptions.

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Fedor Stonyakin. 2019-11-19. Adaptive Gradient Methods for Some Classes of Non-Smooth Optimization Problems. https://arxiv.org/abs/1911.08425

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