Related papers: Adaptive Mirror Descent Methods for Convex Program…
In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming…
This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…
In this paper, we study the convergence of an interior subgradient and proximal methods for a DC (difference of convex functions) constrained minimization problem.
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…
We propose a new family of subgradient- and gradient-based methods which converges with optimal complexity for convex optimization problems whose feasible region is simple enough. This includes cases where the objective function is…
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 condition, but it must necessarily have the Lipshitz-continuous…
We study the unconstrained and the minimax saddle point variants of the convex multi-stage stochastic programming problem, where consecutive decisions are coupled through the objective functions, rather than through the constraints. We…
This paper proposes a new steepest gradient descent method for solving nonconvex finite minimax problems using non-monotone adaptive step sizes and providing proof of convergence results in cases of the nonconvex, quasiconvex, and…
Mirror descent is a well established tool for solving convex optimization problems with convex constraints. This article introduces continuous-time mirror descent dynamics for approximating optimal Markov controls for stochastic control…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
We study two variants of the mirror descent-ascent (MDA) algorithm for solving min-max problems on the space of measures: simultaneous and alternating. We work under assumptions of convexity-concavity and relative smoothness of the payoff…
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…
Distributed gradient descent algorithms have come to the fore in modern machine learning, especially in parallelizing the handling of large datasets that are distributed across several workers. However, scant attention has been paid to…
We investigate different randomizations for mirror descent method. We try to propose such a randomization that allows us to use sparsity of the problem as much as it possible. In the paper one can also find a generalization of randomizaed…
Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of…
Inspired by the recent paper (L. Ying, Mirror descent algorithms for minimizing interacting free energy, Journal of Scientific Computing, 84 (2020), pp. 1-14),we explore the relationship between the mirror descent and the variable metric…
The part of the analysis of the convergence rate of the mirror descent method that is connected with the adaptive time-varying step size rules due to Alkousa et al. (MOTOR 2024, pp. 3-18) is corrected. Moreover, a Lipschitz-free mirror…
We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.
We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…