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In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…

Optimization and Control · Mathematics 2022-09-13 Aleksandr Beznosikov , Abdurakhmon Sadiev , Alexander Gasnikov

The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…

Artificial Intelligence · Computer Science 2013-02-21 Helene Fargier , Jerome Lang , Roger Martin-Clouaire , Thomas Schiex

Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-gap statement says that for a structured set of words -- such…

Information Theory · Computer Science 2026-05-11 Chen Yuan , Ruiqi Zhu

In this paper, we study saddle point (SP) problems, focusing on convex-concave optimization involving functions that satisfy either two-sided quadratic functional growth (QFG) or two-sided quadratic gradient growth (QGG)--novel conditions…

Optimization and Control · Mathematics 2025-10-15 Cody Melcher , Afrooz Jalilzadeh , Erfan Yazdandoost Hamedani

We study the \emph{Proximal Alternating Predictor-Corrector} (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle to solve nonsmooth structured convex-concave saddle point problems consisting of the sum of a smooth convex…

Optimization and Control · Mathematics 2018-09-24 D. Russell Luke , Ron Shefi

This paper studies quasi-Newton methods for solving strongly-convex-strongly-concave saddle point problems (SPP). We propose greedy and random Broyden family updates for SPP, which have explicit local superlinear convergence rate of…

Optimization and Control · Mathematics 2022-04-12 Chengchang Liu , Luo Luo

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

Machine Learning · Statistics 2015-11-24 Zhanxing Zhu , Amos J. Storkey

Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…

Optimization and Control · Mathematics 2021-12-13 Yafei Wang , Bo Pan , Wei Tu , Peng Liu , Bei Jiang , Chao Gao , Wei Lu , Shangling Jui , Linglong Kong

We study solution methods for (strongly-)convex-(strongly)-concave Saddle-Point Problems (SPPs) over networks of two type - master/workers (thus centralized) architectures and meshed (thus decentralized) networks. The local functions at…

Optimization and Control · Mathematics 2022-08-23 Aleksandr Beznosikov , Gesualdo Scutari , Alexander Rogozin , Alexander Gasnikov

Chance constrained programming (CCP) refers to a type of optimization problem with uncertain constraints that are satisfied with at least a prescribed probability level. In this work, we study the sample average approximation (SAA) of…

Optimization and Control · Mathematics 2025-04-30 Peng Wang , Rujun Jiang , Qingyuan Kong , Laura Balzano

This paper studies the complexity of finding approximate stationary points for the smooth nonconvex-strongly-concave (NC-SC) saddle point problem: $\min_x\max_yf(x,y)$. Under the standard first-order smoothness conditions where $f$ is…

Optimization and Control · Mathematics 2024-12-10 Nuozhou Wang , Junyu Zhang , Shuzhong Zhang

In this paper, we consider nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We propose a Trust-Region Stochastic Sequential Quadratic Programming (TR-SSQP) method and establish its…

Optimization and Control · Mathematics 2026-04-02 Yuchen Fang , Javad Lavaei , Sen Na

The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some…

Optimization and Control · Mathematics 2023-11-22 Alexander Titov , Fedor Stonyakin , Mohammad Alkousa , Alexander Gasnikov

Since their introduction, anchoring methods in extragradient-type saddlepoint problems have inspired a flurry of research due to their ability to provide order-optimal rates of accelerated convergence in very general problem settings. Such…

Optimization and Control · Mathematics 2025-06-10 James Alcala , Yat Tin Chow , Mahesh Sunkula

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general…

Optimization and Control · Mathematics 2018-04-11 Antonin Chambolle , Matthias J. Ehrhardt , Peter Richtárik , Carola-Bibiane Schönlieb

In this work, we conduct the first systematic study of stochastic variational inequality (SVI) and stochastic saddle point (SSP) problems under the constraint of differential privacy (DP). We propose two algorithms: Noisy Stochastic…

Optimization and Control · Mathematics 2022-04-04 Digvijay Boob , Cristóbal Guzmán

We investigate the problem of finding second-order stationary points (SOSP) in differentially private (DP) stochastic non-convex optimization. Existing methods suffer from two key limitations: (i) inaccurate convergence error rate due to…

Machine Learning · Computer Science 2026-01-21 Youming Tao , Zuyuan Zhang , Dongxiao Yu , Xiuzhen Cheng , Falko Dressler , Di Wang

In this paper, we explore a broad class of constrained saddle point problems with a bilevel structure, wherein the upper-level objective function is nonconvex-concave and smooth over compact and convex constraint sets, subject to a strongly…

Optimization and Control · Mathematics 2025-03-31 Mohammad Mahdi Ahmadi , Erfan Yazdandoost Hamedani

This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally…

Optimization and Control · Mathematics 2019-07-11 Songtao Lu , Meisam Razaviyayn , Bo Yang , Kejun Huang , Mingyi Hong