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In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Andrei Patrascu

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

Optimization and Control · Mathematics 2020-01-22 Mohammad S. Alkousa

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we…

Optimization and Control · Mathematics 2024-02-13 Jeongyeol Kwon , Dohyun Kwon , Stephen Wright , Robert Nowak

Simple bilevel problems are optimization problems in which we want to find an optimal solution to an inner problem that minimizes an outer objective function. Such problems appear in many machine learning and signal processing applications…

Optimization and Control · Mathematics 2022-12-21 Lior Doron , Shimrit Shtern

We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…

Optimization and Control · Mathematics 2013-08-28 Ting Kei Pong

An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…

Optimization and Control · Mathematics 2019-02-28 S. Gratton , E. Simon , Ph. L. Toint

The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function $F(w)=\frac{1}{n}…

Optimization and Control · Mathematics 2019-04-24 Lam M. Nguyen , Marten van Dijk , Dzung T. Phan , Phuong Ha Nguyen , Tsui-Wei Weng , Jayant R. Kalagnanam

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…

Optimization and Control · Mathematics 2020-12-02 Qihang Lin , Runchao Ma , Yangyang Xu

First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…

Optimization and Control · Mathematics 2025-10-06 Endrit Dosti , Sergiy A. Vorobyov , Themistoklis Charalambous

In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…

Optimization and Control · Mathematics 2019-10-10 Andrei Kulunchakov , Julien Mairal

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

In this paper some adaptive mirror descent algorithms for problems of minimization convex objective functional with several convex Lipschitz (generally, non-smooth) functional constraints are considered. It is shown that the methods are…

Optimization and Control · Mathematics 2018-12-20 F. S. Stonyakin , M . S. Alkousa , A. A. Titov

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

Optimization and Control · Mathematics 2024-12-03 Ion Necoara , Nitesh Kumar Singh

In this paper, we propose a novel accelerated forward-backward splitting algorithm for minimizing convex composite functions, written as the sum of a smooth function and a (possibly) nonsmooth function. When the objective function is…

Optimization and Control · Mathematics 2025-09-19 Kansei Ushiyama

We present in this paper two different classes of general $K$-splitting algorithms for solving finite-dimensional convex optimization problems. Under the assumption that the function being minimized has a Lipschitz continuous gradient, we…

Optimization and Control · Mathematics 2015-03-13 Donald Goldfarb , Shiqian Ma

This paper proposes a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy focuses on solving the problem of Lipschitz constant being unknown. It allows estimate parameter…

Optimization and Control · Mathematics 2024-12-31 Chengzhi Huang , Jian Chen , Liping Tang

This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…

Optimization and Control · Mathematics 2016-05-02 Masoud Ahookhosh

In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the…

Optimization and Control · Mathematics 2017-02-15 Shoham Sabach , Shimrit Shtern

This paper considers the nonconvex nonsmooth problem in which the objective function is Lipschitz continuous. We focus on the stochastic setting where the algorithm can access stochastic function value evaluations with heavy-tailed noise,…

Machine Learning · Computer Science 2026-05-26 Zhuanghua Liu , Luo Luo

We present a variant of accelerated gradient descent algorithms, adapted from Nesterov's optimal first-order methods, for weakly-quasi-convex and weakly-quasi-strongly-convex functions. We show that by tweaking the so-called estimate…

Optimization and Control · Mathematics 2020-06-16 Jingjing Bu , Mehran Mesbahi