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In this paper, for a convex-concave bilinear saddle point problem, we propose a Tikhonov regularized second-order primal-dual dynamical system with slow damping, extrapolation and general time scaling parameters. Depending on the vanishing…

Optimization and Control · Mathematics 2024-09-10 Xiangkai Sun , Liang He , Xian-Jun Long

In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…

Optimization and Control · Mathematics 2023-04-18 Aleksandr Beznosikov , Alexander Gasnikov , Karina Zainulina , Alexander Maslovskiy , Dmitry Pasechnyuk

The primal-dual hybrid gradient (PDHG) method is one of the most popular algorithms for solving saddle point problems. However, when applying the PDHG method and its many variants to some real-world models commonly encountered in signal…

Optimization and Control · Mathematics 2025-06-10 Jintao Yu , Hongjin He

In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable…

Optimization and Control · Mathematics 2025-06-03 Hongjin He , Kai Wang , Jintao Yu

In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…

Optimization and Control · Mathematics 2015-11-16 Cong Dang , Guanghui Lan

We study an inexact inner-outer generalized Golub-Kahan algorithm for the solution of saddle-point problems with a two-times-two block structure. In each outer iteration, an inner system has to be solved which in theory has to be done…

Numerical Analysis · Mathematics 2024-05-15 Vincent Darrigrand , Andrei Dumitrasc , Carola Kruse , Ulrich Ruede

We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method…

Numerical Analysis · Mathematics 2010-06-10 Fred Wubs , Jonas Thies

We revisit the smooth convex-concave bilinearly-coupled saddle-point problem of the form $\min_x\max_y f(x) + \langle y,\mathbf{B} x\rangle - g(y)$. In the highly specific case where each of the functions $f(x)$ and $g(y)$ is either affine…

Optimization and Control · Mathematics 2024-11-25 Dmitry Kovalev , Ekaterina Borodich

Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At the same time, in some applications…

Optimization and Control · Mathematics 2021-09-07 Abdurakhmon Sadiev , Aleksandr Beznosikov , Pavel Dvurechensky , Alexander Gasnikov

This paper considers continuous-time coordination algorithms for networks of agents that seek to collectively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure. Our algorithm design…

Optimization and Control · Mathematics 2017-05-17 Simon K. Niederländer , Jorge Cortés

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

Saddle point problems arise from many wireless applications, and primal-dual iterative algorithms are widely applied to find the saddle points. In the existing literature, the convergence results of such algorithms are established assuming…

Information Theory · Computer Science 2017-04-26 Junting Chen , Vincent K. N. Lau

Saddle-point or primal-dual methods have recently attracted renewed interest as a systematic technique to design distributed algorithms which solve convex optimization problems. When implemented online for streaming data or as dynamic…

Optimization and Control · Mathematics 2021-04-22 John W. Simpson-Porco , Bala Kameshwar Poolla , Nima Monshizadeh , Florian Dorfler

In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming…

Optimization and Control · Mathematics 2022-09-19 Moslem Zamani , Hadi Abbaszadehpeivasti , Etienne de Klerk

In this paper, we design an inertial accelerated primal-dual algorithm to address the convex-concave saddle point problem, which is formulated as $\min_{x}\max_{y} f(x) + \langle Kx, y \rangle - g(y)$. Remarkably, both functions $f$ and $g$…

Optimization and Control · Mathematics 2024-04-17 X. He , N. J. Huang , Y. P. Fang

In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method…

Optimization and Control · Mathematics 2018-05-08 Bui Van Dinh , Nguyen Ngoc Hai , Do Sang Kim

The discretization of Cahn-Hilliard equation with obstacle potential leads to a block 2 by 2 non-linear system, where the p1, 1q block has a non-linear and non-smooth term. Recently a globally convergent Newton Schur method was proposed for…

Numerical Analysis · Computer Science 2021-09-22 Pawan Kumar

We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assume that the sequence of our step sizes is not summable but…

Optimization and Control · Mathematics 2023-05-26 Hui Ouyang

We generalize the well-known primal-dual algorithm proposed by Chambolle and Pock for saddle point problems, and improve the condition for ensuring its convergence. The improved convergence-guaranteeing condition is effective for the…

Optimization and Control · Mathematics 2021-12-02 Bingsheng He , Feng Ma , Shengjie Xu , Xiaoming Yuan

In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…

Optimization and Control · Mathematics 2022-11-01 A. A. Titov , S. S. Ablaev , M. S. Alkousa , F. S. Stonyakin , A. V. Gasnikov