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In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

Optimization and Control · Mathematics 2020-03-10 Ion Necoara

We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror…

In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…

Optimization and Control · Mathematics 2024-01-11 Angelia Nedich , Ion Necoara

The paper presents a new descent algorithm for locally Lipschitz continuous functions $f:X\to\mathbb{R}$. The selection of a descent direction at some iteration point $x$ combines an approximation of the set-valued gradient of $f$ on a…

Numerical Analysis · Mathematics 2019-10-25 Jan Mankau , Friedemann Schuricht

We study differentiable strongly quasiconvex functions for providing new properties for algorithmic and monotonicity purposes. Furthemore, we provide insights into the decreasing behaviour of strongly quasiconvex functions, applying this…

Optimization and Control · Mathematics 2024-10-07 Felipe Lara , Raúl T. Marcavillaca , Phan T. Vuong

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…

Optimization and Control · Mathematics 2016-08-19 Masaru Ito , Mituhiro Fukuda

In the development of first-order methods for smooth (resp., composite) convex optimization problems, where smooth functions with Lipschitz continuous gradients are minimized, the gradient (resp., gradient mapping) norm becomes a…

Optimization and Control · Mathematics 2020-10-06 Masaru Ito , Mituhiro Fukuda

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…

Optimization and Control · Mathematics 2025-06-04 Deven Sethi , David Šiška

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…

Optimization and Control · Mathematics 2017-06-20 Quang Van Nguyen , Olivier Fercoq , Volkan Cevher

This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…

Optimization and Control · Mathematics 2023-08-17 Vladimir Norkin , Alois Pichler , Anton Kozyriev

This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…

Optimization and Control · Mathematics 2025-11-11 Vladimir Solodkin , Andrew Veprikov , Aleksandr Beznosikov

It is widely recognized in modern machine learning practice that access to a diverse set of tasks can enhance performance across those tasks. This observation suggests that, unlike in general multi-objective optimization, the objectives in…

Machine Learning · Computer Science 2025-09-09 Ben Kretzu , Karen Ullrich , Yonathan Efroni

In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…

Optimization and Control · Mathematics 2024-01-10 Flavia Chorobura , Ion Necoara

Smoothness is crucial for attaining fast rates in first-order optimization. However, many optimization problems in modern machine learning involve non-smooth objectives. Recent studies relax the smoothness assumption by allowing the…

Optimization and Control · Mathematics 2026-02-11 Dingzhi Yu , Wei Jiang , Hongyi Tao , Yuanyu Wan , Lijun Zhang

We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds…

Statistics Theory · Mathematics 2019-07-08 Anatoli Juditsky , Alexander Nazin , Arkadi Nemirovsky , Alexandre Tsybakov

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…

Optimization and Control · Mathematics 2016-12-12 Anton Anikin , Alexander Gasnikov , Alexander Gornov

In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally…

Optimization and Control · Mathematics 2023-06-29 Luis M. Briceno-Arias , Francisco José Silva , Xianjin Yang

Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…

Optimization and Control · Mathematics 2025-10-06 Mateo Díaz , Liwei Jiang , Abdel Ghani Labassi

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…

Optimization and Control · Mathematics 2013-07-09 Angelia Nedich , Soomin Lee

An adaptive regularization algorithm for unconstrained nonconvex optimization is presented in which the objective function is never evaluated, but only derivatives are used. This algorithm belongs to the class of adaptive regularization…

Optimization and Control · Mathematics 2022-05-05 S. Gratton , S. Jerad , Ph. L. Toint