15 citations · 31 across the 13 of their papers we have counts for
14 papers
Online Optimization Problems with Functional Constraints under Relative Lipschitz Continuity and Relative Strong Convexity Conditions
Oleg Savchuk, Fedor Stonyakin, Mohammad Alkousa +3
Recently, there were introduced important classes of relatively smooth, relatively continuous, and relatively strongly convex optimization problems. These concepts have significant…
Some Adaptive First-order Methods for Variational Inequalities with Relatively Strongly Monotone Operators and Generalized Smoothness
A. A. Titov, S. S. Ablaev, M. S. Alkousa +2
In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the rec…
Optimization in complex spaces with the Mixed Newton Method
Sergey Bakhurin, Roland Hildebrand, Mohammad Alkousa +2
We propose a second-order method for unconditional minimization of functions of complex arguments. We call it the Mixed Newton Method due to the use of the mixed Wirtinger d…
Some Methods for Relatively Strongly Monotone Variational Inequalities
F. S. Stonyakin, A. A. Titov, D. V. Makarenko +1
The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variatio…
Adaptive Algorithms for Relatively Lipschitz Continuous Convex Optimization Problems
Fedor Stonyakin, Alexander Titov, Mohammad Alkousa +2
Recently there were proposed some innovative convex optimization concepts, namely, relative smoothness [1] and relative strong convexity [2,3]. These approaches have significantly…
Algorithm for solving variational inequalities with relatively strongly monotone operators
Alexander A. Titov
Basing on some recently proposed methods for solving variational inequalities with non-smooth operators, we propose an analogue of the Mirror Prox method for the corresponding clas…
Algorithms for solving variational inequalities and saddle point problems with some generalizations of Lipschitz property for operators
Alexander Titov, Fedor Stonyakin, Mohammad Alkousa +1
The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness condit…
Analogues of Switching Subgradient Schemes for Relatively Lipschitz-Continuous Convex Programming Problems
Alexander Titov, Fedor Stonyakin, Mohammad Alkousa +2
Recently some specific classes of non-smooth and non-Lipschitz convex optimization problems were selected by Yu.~Nesterov along with H.~Lu. We consider convex programming problems…
Mirror Descent for Constrained Optimization Problems with Large Subgradient Values
Fedor Stonyakin, Alexey Stepanov, Alexander Gasnikov +1
Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional with non-positive convex (generally, non-smooth)…
On Some Adaptive Mirror Descent Algorithms for Convex and Strongly Convex Optimization Problems with Functional Constraints
F. S. Stonyakin, M . S. Alkousa, A. A. Titov
In this paper some adaptive mirror descent algorithms for problems of minimization convex objective functional with several convex Lipschitz (generally, non-smooth) functional cons…
Mirror Descent and Constrained Online Optimization Problems
Alexander Titov, Fedor Stonyakin, Alexander Gasnikov +1
We consider the following class of online optimization problems with functional constraints. Assume, that a finite set of convex Lipschitz-continuous non-smooth functionals are giv…
Generalized Mirror Prox for Monotone Variational Inequalities: Universality and Inexact Oracle
Fedor Stonyakin, Alexander Gasnikov, Pavel Dvurechensky +2
We introduce an inexact oracle model for variational inequalities (VI) with monotone operator, propose a numerical method which solves such VI's and analyze its convergence rate. A…
One Mirror Descent Algorithm for Convex Constrained Optimization Problems with non-standard growth properties
Fedor S. Stonyakin, Alexander A. Titov
The paper is devoted to a special Mirror Descent algorithm for problems of convex minimization with functional constraints. The objective function may not satisfy the Lipschitz con…
Mirror Descent and Convex Optimization Problems With Non-Smooth Inequality Constraints
Anastasia Bayandina, Pavel Dvurechensky, Alexander Gasnikov +2
We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in…