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In recent years, nonconvex minimax problems have attracted significant attention due to their broad applications in machine learning, including generative adversarial networks, robust optimization and adversarial training. Most existing…

Optimization and Control · Mathematics 2026-03-06 Yan Gao , Yongchao Liu

In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…

Optimization and Control · Mathematics 2020-05-26 Parvin Nazari , Davoud Ataee Tarzanagh , George Michailidis

This paper investigates the stochastic distributed nonconvex optimization problem of minimizing a global cost function formed by the summation of $n$ local cost functions. We solve such a problem by involving zeroth-order (ZO) information…

Optimization and Control · Mathematics 2021-10-15 Shengjun Zhang , Yunlong Dong , Dong Xie , Lisha Yao , Colleen P. Bailey , Shengli Fu

We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy…

Machine Learning · Statistics 2018-03-26 Yining Wang , Sivaraman Balakrishnan , Aarti Singh

Supported by the recent contributions in multiple branches, the first-order splitting algorithms became central for structured nonsmooth optimization. In the large-scale or noisy contexts, when only stochastic information on the smooth part…

Optimization and Control · Mathematics 2020-10-05 Andrei Patrascu , Paul Irofti

We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…

Optimization and Control · Mathematics 2024-11-05 Jelena Diakonikolas , Cristóbal Guzmán

In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…

Optimization and Control · Mathematics 2026-03-03 Mohammad S. Alkousa , Fedor S. Stonyakin

In this paper, we consider a stochastic distributed nonconvex optimization problem with the cost function being distributed over $n$ agents having access only to zeroth-order (ZO) information of the cost. This problem has various machine…

Optimization and Control · Mathematics 2022-01-11 Xinlei Yi , Shengjun Zhang , Tao Yang , Karl H. Johansson

This paper considers decentralized nonsmooth nonconvex optimization problem with Lipschitz continuous local functions. We propose an efficient stochastic first-order method with client sampling, achieving the $(\delta,\epsilon)$-Goldstein…

Optimization and Control · Mathematics 2026-01-28 Xinyan Chen , Weiguo Gao , Luo Luo

In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization term. Moreover, only the function values for the…

Optimization and Control · Mathematics 2024-01-09 Shanglin Liu , Lei Wang , Nachuan Xiao , Xin Liu

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

We introduce a new zeroth-order algorithm for private stochastic optimization on nonconvex and nonsmooth objectives. Given a dataset of size $M$, our algorithm ensures $(\alpha,\alpha\rho^2/2)$-R\'enyi differential privacy and finds a…

Optimization and Control · Mathematics 2024-07-01 Qinzi Zhang , Hoang Tran , Ashok Cutkosky

Zeroth-order (ZO) optimization with ordinal feedback has emerged as a fundamental problem in modern machine learning systems, particularly in human-in-the-loop settings such as reinforcement learning from human feedback, preference…

Optimization and Control · Mathematics 2025-12-23 Haishan Ye

In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the…

Optimization and Control · Mathematics 2012-07-16 Radu Ioan Bot , Christopher Hendrich

The usual approach to developing and analyzing first-order methods for non-smooth (stochastic or deterministic) convex optimization assumes that the objective function is uniformly Lipschitz continuous with parameter $M_f$. However, in many…

Optimization and Control · Mathematics 2018-08-15 Haihao Lu

We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…

Optimization and Control · Mathematics 2018-09-25 John Duchi , Feng Ruan

Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of…

Machine Learning · Statistics 2020-01-28 Huizhuo Yuan , Xiangru Lian , Ji Liu

We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…

Optimization and Control · Mathematics 2024-05-20 Andrzej Ruszczyński , Shangzhe Yang

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

Optimization and Control · Mathematics 2019-01-25 Ching-pei Lee , Stephen J. Wright

We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…

Optimization and Control · Mathematics 2019-05-17 Radu Ioan Bot , Axel Böhm