Fetching the paper…
Reading the bibliography…
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 different situations: smooth or non-smooth objective function; convex or strongly convex objective and constraint; deterministic or randomized information about the objective and constraint.
Existence theorems and convergence of minimizing sequences in extremum problems with restrictions
B. Polyak · 1967
Earlier work this paper cites.
A general method of solving extremum problems
B. Polyak · 1967
Earlier work this paper cites.
Generalized gradient descent with application to block programming
N. Z. Shor · 1967
Earlier work this paper cites.
Efficient methods for large-scale convex optimization problems
A. Nemirovskii · 1979
Earlier work this paper cites.
Problem Complexity and Method Efficiency in Optimization
A. Nemirovsky and D. Yudin · 1983
Earlier work this paper cites.
A method of solving a convex programming problem with convergence rate o ( 1 / k 2 ) o(1/k^{2})
Y. Nesterov · 1983
Earlier work this paper cites.
Optimal methods of smooth convex minimization
A. Nemirovskii and Y. Nesterov · 1985
Earlier work this paper cites.
Lectures on Modern Convex Optimization
A. Ben-Tal and A. Nemirovski · 2001
Earlier work this paper cites.
Mirror descent and nonlinear projected subgradient methods for convex optimization
A. Beck and M. Teboulle · 2003
Earlier work this paper cites.
Introductory Lectures on Convex Optimization: a basic course
Y. Nesterov · 2004
Earlier work this paper cites.
Primal-dual subgradient methods for convex problems
Y. Nesterov · 2005
Cited alongside, same era.
Robust stochastic approximation approach to stochastic programming
A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro · 2009
Cited alongside, same era.
The comirror algorithm for solving nonsmooth constrained convex problems
A. Beck, A. Ben-Tal, N. Guttmann-Beck, and L. Tetruashvili · 2010
Cited alongside, same era.
Optimization methods. Optimality conditions in extremal problems
A. Birjukov · 2010
Cited alongside, same era.
Composite objective mirror descent
J. Duchi, S. Shalev-Shwartz, Y. Singer, and A. Tewari · 2010
Cited alongside, same era.
Dual averaging methods for regularized stochastic learning and online optimization
L. Xiao · 2010
Lectures on Modern Convex Optimization (Lecture Notes)
A. Ben-Tal and A. Nemirovski · 2015
Later among the works it cites.
New primal-dual subgradient methods for convex problems with functional constraints, 2015
Y. Nesterov · 2015
Later among the works it cites.
Randomization and sparsity in huge-scale optimization on an example of mirror descent
A. Anikin, A. Gasnikov, and A. Gornov · 2016
Later among the works it cites.
Algorithms for stochastic optimization with expectation constraints
G. Lan and Z. Zhou · 2016
Later among the works it cites.
Subgradient methods for convex functions with nonstandard growth properties, 2016
Y. Nesterov · 2016
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
First order methods for non-smooth convex large-scale optimization, i: General purpose methods
A. Juditsky and A. Nemirovski · 2012
Cited alongside, same era.
Concentration Inequalities: A Nonasymptotic Theory of Independence
S. Boucheron, G. Lugosi, and P. Massart · 2013
Cited alongside, same era.
Deterministic and stochastic primal-dual subgradient algorithms for uniformly convex minimization
A. Juditsky and Y. Nesterov · 2014
Cited alongside, same era.
On stochastic subgradient mirror-descent algorithm with weighted averaging
A. Nedic and S. Lee · 2014
Cited alongside, same era.
Adaptive mirror descent for constrained optimization
A. Bayandina · 2017
Closest in time.
Adaptive stochastic mirror descent for constrained optimization
A. Bayandina · 2017
Closest in time.
Sharpness, restart and acceleration
V. Roulet and A. d’Aspremont · 2017
Closest in time.
Primal-dual mirror descent for the stochastic programming problems with functional constraints
A. Bayandina, A. Gasnikov, E. Gasnikova, and S. Matsievsky · 2018
Closest in time.