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Inspired by the Optimistic Gradient Ascent-Proximal Point Algorithm (OGAProx) proposed by Bo{\c{t}}, Csetnek, and Sedlmayer for solving a saddle-point problem associated with a convex-concave function with a nonsmooth coupling function and…

Optimization and Control · Mathematics 2023-11-01 Hui Ouyang

This paper proposes an adaptive primal-dual dynamics for distributed optimization in multi-agent systems. The proposed dynamics incorporates an adaptive synchronization law that reinforces the interconnection strength between the primal…

Optimization and Control · Mathematics 2019-05-03 P. A. Bansode , K. C. Kosaraju , S. R. Wagh , R. Pasumarthy , N. M. Singh

In this paper, we focus on solving a class of constrained non-convex non-concave saddle point problems in a decentralized manner by a group of nodes in a network. Specifically, we assume that each node has access to a summand of a global…

Optimization and Control · Mathematics 2019-11-01 Weijie Liu , Aryan Mokhtari , Asuman Ozdaglar , Sarath Pattathil , Zebang Shen , Nenggan Zheng

For the inclusion problem involving two maximal monotone operators, under the metric subregularity of the composite operator, we derive the linear convergence of the generalized proximal point algorithm and several splitting algorithms,…

Optimization and Control · Mathematics 2016-09-28 Li Shen , Shaohua Pan

Hyper-parameter optimization remains as the core issue of Gaussian process (GP) for machine learning nowadays. The benchmark method using maximum likelihood (ML) estimation and gradient descent (GD) is impractical for processing big data…

Machine Learning · Statistics 2019-06-10 Linning Xu , Feng Yin , Jiawei Zhang , Zhi-Quan Luo , Shuguang Cui

We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…

Machine Learning · Computer Science 2016-11-04 P Balamurugan , Francis Bach

Methods with adaptive scaling of different features play a key role in solving saddle point problems, primarily due to Adam's popularity for solving adversarial machine learning problems, including GANS training. This paper carries out a…

Machine Learning · Computer Science 2023-06-22 Aleksandr Beznosikov , Aibek Alanov , Dmitry Kovalev , Martin Takáč , Alexander Gasnikov

We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in…

Optimization and Control · Mathematics 2021-12-23 Antonio Silveti-Falls , Cesare Molinari , Jalal Fadili

In this paper we combine the stochastic variance reduced gradient (SVRG) method [17] with the primal dual fixed point method (PDFP) proposed in [7] to solve a sum of two convex functions and one of which is linearly composite. This type of…

Optimization and Control · Mathematics 2020-07-24 Ya-Nan Zhu , Xiaoqun Zhang

We derive an extension of the sequential homotopy method that allows for the application of inexact solvers for the linear (double) saddle-point systems arising in the local semismooth Newton method for the homotopy subproblems. For the…

Optimization and Control · Mathematics 2023-11-30 John W. Pearson , Andreas Potschka

This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…

Optimization and Control · Mathematics 2022-11-15 Killian Wood , Emiliano Dall'Anese

We propose a regularized saddle-point algorithm for convex networked optimization problems with resource allocation constraints. Standard distributed gradient methods suffer from slow convergence and require excessive communication when…

Systems and Control · Computer Science 2012-08-16 Andrea Simonetto , Tamas Keviczky , Mikael Johansson

Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…

Optimization and Control · Mathematics 2024-02-08 Xufeng Cai , Cheuk Yin Lin , Jelena Diakonikolas

In this paper, we investigate a class of constrained saddle point (SP) problems where the objective function is nonconvex-concave and smooth. This class of problems has wide applicability in machine learning, including robust multi-class…

Optimization and Control · Mathematics 2023-11-02 Morteza Boroun , Erfan Yazdandoost Hamedani , Afrooz Jalilzadeh

The primal-dual method of multipliers (PDMM) was originally designed for solving a decomposable optimisation problem over a general network. In this paper, we revisit PDMM for optimisation over a centralized network. We first note that the…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-07-21 Guoqiang Zhang , Kenta Niwa , W. Bastiaan Kleijn

Classical primal-dual algorithms attempt to solve $\max_{\mu}\min_{x} \mathcal{L}(x,\mu)$ by alternatively minimizing over the primal variable $x$ through primal descent and maximizing the dual variable $\mu$ through dual ascent. However,…

Optimization and Control · Mathematics 2023-11-20 Kaizhao Sun , Andy Sun

This paper focuses on the decentralized optimization (minimization and saddle point) problems with objective functions that satisfy Polyak-{\L}ojasiewicz condition (PL-condition). The first part of the paper is devoted to the minimization…

Optimization and Control · Mathematics 2024-05-14 Ilya Kuruzov , Mohammad Alkousa , Fedor Stonyakin , Alexander Gasnikov

The primal-dual Douglas-Rachford method is a well-known algorithm to solve optimization problems written as convex-concave saddle-point problems. Each iteration involves solving a linear system involving a linear operator and its adjoint.…

Optimization and Control · Mathematics 2025-11-11 Emanuele Naldi , Felix Schneppe

In this paper, we extend the inexact Uzawa algorithm in [Q. Hu, J. Zou, SIAM J. Matrix Anal., 23(2001), pp. 317-338] to the nonsymmetric generalized saddle point problem. The techniques used here are similar to those in [Bramble \emph{et…

Numerical Analysis · Mathematics 2014-08-26 Hailun Shen , Hua Xiang

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