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Sparsity-inducing regularization problems are ubiquitous in machine learning applications, ranging from feature selection to model compression. In this paper, we present a novel stochastic method -- Orthant Based Proximal Stochastic…

Optimization and Control · Mathematics 2020-07-24 Tianyi Chen , Tianyu Ding , Bo Ji , Guanyi Wang , Jing Tian , Yixin Shi , Sheng Yi , Xiao Tu , Zhihui Zhu

We introduce new multilevel methods for solving large-scale unconstrained optimization problems. Specifically, the philosophy of multilevel methods is applied to Newton-type methods that regularize the Newton sub-problem using second order…

Optimization and Control · Mathematics 2024-07-16 Nick Tsipinakis , Panos Parpas

In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general $(L_0, L_1)$-smoothness setting, which gains particular…

Optimization and Control · Mathematics 2025-02-07 Chenghan Xie , Chenxi Li , Chuwen Zhang , Qi Deng , Dongdong Ge , Yinyu Ye

We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…

Optimization and Control · Mathematics 2022-02-10 Yujia Jin , Aaron Sidford , Kevin Tian

The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…

Optimization and Control · Mathematics 2025-11-24 Danqing Zhou , Hongmei Chen , Shiqian Ma , Junfeng Yang

In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…

Functional Analysis · Mathematics 2014-05-22 Ibrahim Karahan , Murat Ozdemir

Coordinate-type subgradient methods for addressing nonsmooth optimization problems are relatively underexplored due to the set-valued nature of the subdifferential. In this work, our study focuses on nonsmooth composite optimization…

Optimization and Control · Mathematics 2023-08-24 Lei Zhao , Ding Chen , Daoli Zhu , Xiao Li

In this paper, we propose some accelerated methods for solving optimization problems under the condition of relatively smooth and relatively Lipschitz continuous functions with an inexact oracle. We consider the problem of minimizing the…

Optimization and Control · Mathematics 2024-11-27 O. S. Savchuk , M. S. Alkousa , A. S. Shushko , A. A. Vyguzov , F. S. Stonyakin , D. A. Pasechnyuk , A. V. Gasnikov

Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable…

Statistics Theory · Mathematics 2013-07-19 Susanne M. Schennach

The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…

Machine Learning · Computer Science 2025-12-24 Zhiyu Liu , Zhi Han , Yandong Tang , Jun Fan , Yao Wang

We introduce subgradient-based Lavrentiev regularisation of the form \begin{equation*} \mathcal{A}(u) + \alpha \partial \mathcal{R}(u) \ni f^\delta \end{equation*} for linear and nonlinear ill-posed problems with monotone operators…

Optimization and Control · Mathematics 2024-10-01 Markus Grasmair , Fredrik Hildrum

Sign-based stochastic methods have gained attention due to their ability to achieve robust performance despite using only the sign information for parameter updates. However, the current convergence analysis of sign-based methods relies on…

Machine Learning · Computer Science 2023-10-24 Tao Sun , Congliang Chen , Peng Qiao , Li Shen , Xinwang Liu , Dongsheng Li

In this paper, we propose a conditional gradient method for solving constrained vector optimization problems with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. When the partial order under…

Optimization and Control · Mathematics 2022-04-12 Wang Chen , Xinmin Yang , Yong Zhao

The Method of Ellipcenters (ME), introduced in~\cite{ME2025} for strongly convex quadratic minimization, uses two gradient evaluations per iteration: one at the current iterate and one at a companion point on the same level set. We extend…

Optimization and Control · Mathematics 2026-05-12 Yunier Bello-Cruz

This paper introduces a novel family of generalized exponentiated gradient (EG) updates derived from an Alpha-Beta divergence regularization function. Collectively referred to as EGAB, the proposed updates belong to the category of…

Machine Learning · Computer Science 2024-12-30 Andrzej Cichocki , Sergio Cruces , Auxiliadora Sarmiento , Toshihisa Tanaka

In this paper, we study the local linear convergence behavior of proximal-gradient (PG) descent algorithm on a parameterized gap-function reformulation of a smooth but non-monotone variational inequality problem (VIP). The aim is to solve…

Optimization and Control · Mathematics 2025-10-15 Lei Zhao , Daoli Zhu , Shuzhong Zhang

The classical analysis of Stochastic Gradient Descent (SGD) with polynomially decaying stepsize $\eta_t = \eta/\sqrt{t}$ relies on well-tuned $\eta$ depending on problem parameters such as Lipschitz smoothness constant, which is often…

Optimization and Control · Mathematics 2023-05-23 Junchi Yang , Xiang Li , Ilyas Fatkhullin , Niao He

We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies…

Machine Learning · Computer Science 2024-12-12 Alexander Tyurin

This paper considers the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on the algebraic variety of real matrices of upper-bounded rank. This problem is known to enable the formulation of various…

Optimization and Control · Mathematics 2026-03-13 Guillaume Olikier , Kyle A. Gallivan , P. -A. Absil

We study gradient methods for optimizing $(L_0, L_1)$-smooth functions, a class that generalizes Lipschitz-smooth functions and has gained attention for its relevance in machine learning. We provide new insights into the structure of this…

Optimization and Control · Mathematics 2025-03-11 Daniil Vankov , Anton Rodomanov , Angelia Nedich , Lalitha Sankar , Sebastian U. Stich
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