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This paper introduces generalized Bregman projection algorithms for solving nonlinear split feasibility problems (SF P s) in infinitedimensional Hilbert spaces. The methods integrate Bregman projections, proximal gradient steps, and…

Optimization and Control · Mathematics 2025-05-20 Saeed Hashemi Sababe , Ehsan Lotfali Ghasab

In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include…

Machine Learning · Computer Science 2020-07-15 Yan Yan , Yi Xu , Lijun Zhang , Xiaoyu Wang , Tianbao Yang

We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the…

Optimization and Control · Mathematics 2021-03-17 Nguyen Van Dung , Băng Công Vũ

In this work, we propose an adaptive variation on the classical Heavy-ball method for convex quadratic minimization. The adaptivity crucially relies on so-called "Polyak step-sizes", which consists in using the knowledge of the optimal…

Optimization and Control · Mathematics 2022-10-13 Baptiste Goujaud , Adrien Taylor , Aymeric Dieuleveut

This paper revisits the Polyak step size schedule for convex optimization problems, proving that a simple variant of it simultaneously attains near optimal convergence rates for the gradient descent algorithm, for all ranges of strong…

Optimization and Control · Mathematics 2022-08-03 Elad Hazan , Sham Kakade

In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…

Optimization and Control · Mathematics 2020-10-06 Francesco Farina , Giuseppe Notarstefano

The convex feasibility problem (CFP) is at the core of the modeling of many problems in various areas of science. Subgradient projection methods are important tools for solving the CFP because they enable the use of subgradient calculations…

Optimization and Control · Mathematics 2017-03-06 Yair Censor , Daniel Reem

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

Optimization and Control · Mathematics 2024-12-10 Howard Heaton

We investigate the convergence of stochastic mirror descent (SMD) under interpolation in relatively smooth and smooth convex optimization. In relatively smooth convex optimization we provide new convergence guarantees for SMD with a…

Optimization and Control · Mathematics 2023-05-26 Ryan D'Orazio , Nicolas Loizou , Issam Laradji , Ioannis Mitliagkas

In this paper, we establish the convergence of the stochastic Heavy Ball (SHB) algorithm under more general conditions than in the current literature. Specifically, (i) The stochastic gradient is permitted to be biased, and also, to have…

Optimization and Control · Mathematics 2025-04-28 Uday Kiran Reddy Tadipatri , Mathukumalli Vidyasagar

This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…

Optimization and Control · Mathematics 2024-06-07 Wei Jiang , Sifan Yang , Wenhao Yang , Yibo Wang , Yuanyu Wan , Lijun Zhang

We consider the minimization of a sum of an expectation-valued coordinate-wise $L_i$-smooth nonconvex function and a nonsmooth block-separable convex regularizer. We propose an asynchronous variance-reduced algorithm, where in each…

Optimization and Control · Mathematics 2020-02-20 Jinlong Lei , Uday V. Shanbhag

We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…

Optimization and Control · Mathematics 2021-08-30 James Renegar , Song Zhou

In 1963 Boris Polyak suggested a particular step size for gradient descent methods, now known as the Polyak step size, that he later adapted to subgradient methods. The Polyak step size requires knowledge of the optimal value of the…

Optimization and Control · Mathematics 2024-04-15 Nikhil Devanathan , Stephen Boyd

Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…

Optimization and Control · Mathematics 2024-03-15 Nazanin Abolfazli , Ruichen Jiang , Aryan Mokhtari , Erfan Yazdandoost Hamedani

The popularity of bi-level optimization (BO) in deep learning has spurred a growing interest in studying gradient-based BO algorithms. However, existing algorithms involve two coupled learning rates that can be affected by approximation…

Machine Learning · Computer Science 2023-11-03 Chen Fan , Gaspard Choné-Ducasse , Mark Schmidt , Christos Thrampoulidis

This work considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in…

Signal Processing · Electrical Eng. & Systems 2020-03-26 Xiao Fu , Shahana Ibrahim , Hoi-To Wai , Cheng Gao , Kejun Huang

The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the…

Optimization and Control · Mathematics 2021-02-25 Shixiang Chen , Alfredo Garcia , Shahin Shahrampour

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

We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…

Optimization and Control · Mathematics 2017-03-03 Alfredo Iusem , Alejandro Jofré , Philip Thompson