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Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

Optimization and Control · Mathematics 2021-07-08 Morteza Boroun , Afrooz Jalilzadeh

In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function to a nonnegative nonsmooth convex function, while the…

Optimization and Control · Mathematics 2025-12-25 Junpeng Zhou , Na Zhang , Qia Li

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

Optimization and Control · Mathematics 2022-03-02 Boris S. Mordukhovich , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

Optimization and Control · Mathematics 2016-08-30 Akhil P T , Rajesh Sundaresan

We consider minimization of the sum of a large number of convex functions, and we propose an incremental aggregated version of the proximal algorithm, which bears similarity to the incremental aggregated gradient and subgradient methods…

Systems and Control · Computer Science 2015-11-05 Dimitri P. Bertsekas

We consider the problem of minimizing the composition of a nonsmooth function with a smooth mapping in the case where the proximity operator of the nonsmooth function can be explicitly computed. We first show that this proximity operator…

Optimization and Control · Mathematics 2023-08-29 Gilles Bareilles , Franck Iutzeler , Jérôme Malick

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…

Numerical Analysis · Mathematics 2016-05-13 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato

This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…

Optimization and Control · Mathematics 2025-04-16 Yunier Bello-Cruz , Max L. N. Gonçalves , Jefferson G. Melo , Cassandra Mohr

Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…

Optimization and Control · Mathematics 2023-11-20 Alessandro Scagliotti , Piero Colli Franzone

In this paper we consider finite sum composite convex optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the…

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

In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…

Numerical Analysis · Mathematics 2019-07-11 Jianchao Bai , Ke Guo , Xiaokai Chang

In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational…

Optimization and Control · Mathematics 2021-06-28 Anton Rodomanov , Yurii Nesterov

In this paper, we study the proximal incremental aggregated gradient(PIAG) algorithm for minimizing the sum of L-smooth nonconvex component functions and a proper closed convex function. By exploiting the L-smooth property and with the help…

Optimization and Control · Mathematics 2020-06-01 Wei Peng , Hui Zhang , Xiaoya Zhang

We consider the problem of minimizing the sum of three convex functions: i) a smooth function $f$ in the form of an expectation or a finite average, ii) a non-smooth function $g$ in the form of a finite average of proximable functions…

Optimization and Control · Mathematics 2022-03-25 Konstantin Mishchenko , Peter Richtárik

We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods…

Machine Learning · Statistics 2014-03-19 Jason D. Lee , Yuekai Sun , Michael A. Saunders

We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…

Machine Learning · Computer Science 2013-01-23 Hua Ouyang , Niao He , Alexander Gray

We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…

The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self-concordant-like property, this concept…

Optimization and Control · Mathematics 2018-01-23 Quoc Tran-Dinh , Yen-Huan Li , Volkan Cevher

We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…

Optimization and Control · Mathematics 2024-07-11 Alberto De Marchi , Andreas Themelis

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Machine Learning · Computer Science 2024-01-24 Alexandre d'Aspremont , Cristóbal Guzmán , Clément Lezane