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Many convex optimization problems have structured objective function written as a sum of functions with different types of oracles (full gradient, coordinate derivative, stochastic gradient) and different evaluation complexity of these…

In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…

Optimization and Control · Mathematics 2015-10-27 Saeed Ghadimi , Guanghui Lan , Hongchao Zhang

We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…

Optimization and Control · Mathematics 2026-03-06 Renbo Zhao

We develop universal gradient methods for Stochastic Convex Optimization (SCO). Our algorithms automatically adapt not only to the oracle's noise but also to the H\"older smoothness of the objective function without a priori knowledge of…

Optimization and Control · Mathematics 2024-07-12 Anton Rodomanov , Ali Kavis , Yongtao Wu , Kimon Antonakopoulos , Volkan Cevher

We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…

Optimization and Control · Mathematics 2025-10-14 Harshal D. Kaushik , Ming Jin

We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton's method and the linear conjugate gradient algorithm, with explicit detection and use of negative curvature directions for the…

Optimization and Control · Mathematics 2018-11-14 Clément W. Royer , Michael O'Neill , Stephen J. Wright

In this note we propose a new variant of the hybrid variance-reduced proximal gradient method in [7] to solve a common stochastic composite nonconvex optimization problem under standard assumptions. We simply replace the independent…

Optimization and Control · Mathematics 2020-08-21 Deyi Liu , Lam M. Nguyen , Quoc Tran-Dinh

Motivated by the extensive application of approximate gradients in machine learning and optimization, we investigate inexact subgradient methods subject to persistent additive errors. Within a nonconvex semialgebraic framework, assuming…

Optimization and Control · Mathematics 2025-05-14 Jérôme Bolte , Tam Le , Éric Moulines , Edouard Pauwels

In this paper, we consider Frank-Wolfe-based algorithms for composite convex optimization problems with objective involving a logarithmically-homogeneous, self-concordant functions. Recent Frank-Wolfe-based methods for this class of…

Optimization and Control · Mathematics 2023-10-24 Nimita Shinde , Vishnu Narayanan , James Saunderson

In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…

Optimization and Control · Mathematics 2021-03-24 Nikita Doikov , Yurii Nesterov

We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…

Optimization and Control · Mathematics 2023-11-03 Billy Jin , Katya Scheinberg , Miaolan Xie

This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…

Optimization and Control · Mathematics 2024-09-26 Gregorio M. Sempere , Welington de Oliveira , Johannes O. Royset

In this paper we develop a higher-order method for solving composite (non)convex minimization problems with smooth (non)convex functional constraints. At each iteration our method approximates the smooth part of the objective function and…

Optimization and Control · Mathematics 2025-03-04 Yassine Nabou , Ion Necoara

We focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding…

Optimization and Control · Mathematics 2017-06-21 Jérôme Bolte , Shoham Sabach , Marc Teboulle , Yakov Vaisbourd

Zeroth-order optimization, which does not use derivative information, is one of the significant research areas in the field of mathematical optimization and machine learning. Although various studies have explored zeroth-order algorithms,…

Optimization and Control · Mathematics 2024-07-16 Ryota Nozawa , Pierre-Louis Poirion , Akiko Takeda

Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is to propose a version of the gradient projection algorithm for…

Optimization and Control · Mathematics 2019-06-28 Maxim Balashov , Boris Polyak , Andrey Tremba

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

Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their…

Optimization and Control · Mathematics 2022-10-17 Christian Kanzow , Theresa Lechner

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 analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly…

Optimization and Control · Mathematics 2018-12-04 Zhize Li , Jian Li