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Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…

Optimization and Control · Mathematics 2025-03-04 Ion Necoara , Daniela Lupu

This paper focuses on the problem of minimizing a locally Lipschitz continuous function. Motivated by the effectiveness of Bregman gradient methods in training nonsmooth deep neural networks and the recent progress in stochastic subgradient…

Optimization and Control · Mathematics 2025-06-02 Kuangyu Ding , Kim-Chuan Toh

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…

Optimization and Control · Mathematics 2019-07-04 Stefan Vlaski , Ali H. Sayed

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

We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…

Optimization and Control · Mathematics 2026-03-31 Yuyang Huang , Dante Kalise , Hicham Kouhkouh

Stochastic optimization via Stochastic Gradient Descent (SGD) is a fundamental problem in statistics and optimization. This paper revisits Stochastic Gradient Descent (SGD) for strongly convex objectives, establishing tight, uniform-in-time…

Optimization and Control · Mathematics 2026-03-19 Kang Chen , Yasong Feng , Tianyu Wang

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

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

Optimization and Control · Mathematics 2025-12-12 Chenglong Bao , Yancheng Yuan , Shulan Zhu

Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…

Optimization and Control · Mathematics 2019-05-15 Michael R. Metel , Akiko Takeda

In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…

Optimization and Control · Mathematics 2018-03-12 Andre Milzarek , Xiantao Xiao , Shicong Cen , Zaiwen Wen , Michael Ulbrich

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

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

This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…

Optimization and Control · Mathematics 2026-01-12 Dimitris Boskos , Jorge Cortés , Sonia Martínez

We consider a distributed convex optimization problem in a network which is time-varying and not always strongly connected. The local cost function of each node is affected by some stochastic process. All nodes of the network collaborate to…

Optimization and Control · Mathematics 2021-05-27 Wenjie Li , Mohamad Assaad

In this paper, we consider the general non-oblivious stochastic optimization where the underlying stochasticity may change during the optimization procedure and depends on the point at which the function is evaluated. We develop Stochastic…

Optimization and Control · Mathematics 2020-09-10 Hamed Hassani , Amin Karbasi , Aryan Mokhtari , Zebang Shen

The performance of standard stochastic approximation implementations can vary significantly based on the choice of the steplength sequence, and in general, little guidance is provided about good choices. Motivated by this gap, in the first…

Optimization and Control · Mathematics 2015-03-19 Farzad Yousefian , Angelia Nedić , Uday V. Shanbhag

In this paper, we study ordinary differential equations (ODE) coupled with solutions of a stochastic nonsmooth convex optimization problem (SNCOP). We use the regularization approach, the sample average approximation and the time-stepping…

Optimization and Control · Mathematics 2025-02-11 Jianfeng Luo , Xiaojun Chen

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

Optimization and Control · Mathematics 2016-05-24 Sashank J. Reddi , Suvrit Sra , Barnabas Poczos , Alex Smola

We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic…

Statistics Theory · Mathematics 2021-02-03 Ngoc Huy Chau , Éric Moulines , Miklos Rásonyi , Sotirios Sabanis , Ying Zhang

We study the oracle complexity of nonsmooth nonconvex optimization, with the algorithm assumed to have access only to local function information. It has been shown by Davis, Drusvyatskiy, and Jiang (2023) that for nonsmooth Lipschitz…

Optimization and Control · Mathematics 2024-09-17 Guy Kornowski , Swati Padmanabhan , Ohad Shamir