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This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic $O(1/n)$ convergence rate of our proposed algorithm in…

Optimization and Control · Mathematics 2022-07-21 Olaniyi S. Iyiola , Yekini Shehu

We propose a new primal-dual splitting method for solving composite inclusions involving Lipschitzian, and parallel-sum-type monotone operators. Our approach extends the framework in \cite{Siopt4} to a more general class of monotone…

Optimization and Control · Mathematics 2015-07-28 Quoc Tran-Dinh , Bang Cong Vu

This paper discusses algorithms for solving Markov decision processes (MDPs) that have monotone optimal policies. We propose a two-stage alternating convex optimization scheme that can accelerate the search for an optimal policy by…

Systems and Control · Computer Science 2017-04-04 Robert Mattila , Cristian R. Rojas , Vikram Krishnamurthy , Bo Wahlberg

The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…

Optimization and Control · Mathematics 2025-11-24 Danqing Zhou , Hongmei Chen , Shiqian Ma , Junfeng Yang

The main purpose of this paper is to propose a variance-based Bregman extragradient algorithm with line search for solving stochastic variational inequalities, which is robust with respect an unknown Lipschitz constant. We prove the almost…

Optimization and Control · Mathematics 2022-08-31 Xian-Jun Long , Yue-Hong He , Nan-Jing Huang

We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…

Optimization and Control · Mathematics 2026-03-06 Renbo Zhao

We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from…

Optimization and Control · Mathematics 2024-04-16 M. Marques Alves , João M. Pereira , Benar F. Svaiter

This work presents a universal accelerated first-order primal-dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and H\"{o}lder gradients but does not need to know the smoothness level of the…

Optimization and Control · Mathematics 2022-11-09 Hao Luo

In this paper, we propose universal proximal mirror methods to solve the variational inequality problem with Holder continuous operators in both deterministic and stochastic settings. The proposed methods automatically adapt not only to the…

Optimization and Control · Mathematics 2024-10-07 Anton Klimza , Alexander Gasnikov , Fedor Stonyakin , Mohammad Alkousa

We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…

Optimization and Control · Mathematics 2026-03-31 Guido Tapia-Riera , Camille Castera , Nicolas Papadakis

A new adaptive approach is proposed for variational inequalities with a Lipschitz-continuous field. Estimates of the necessary number of iterations are obtained to achieve a given quality of the variational inequality solution. A…

Optimization and Control · Mathematics 2018-12-27 Fedor Stonyakin , Alexander Gasnikov , Pavel Dvurechensky , Alexander Titov

The proximal point algorithm (PPA) has been developed to solve the monotone variational inequality problem. It provides a theoretical foundation for some methods, such as the augmented Lagrangian method (ALM) and the alternating direction…

Optimization and Control · Mathematics 2023-08-16 Jingyu Gao , Xiurui Geng

When minimizing a multiobjective optimization problem (MOP) using multiobjective gradient descent methods, the imbalances among objective functions often decelerate the convergence. In response to this challenge, we propose two types of the…

Optimization and Control · Mathematics 2023-08-10 Jian Chen , Liping Tang , Xinmin Yang

Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a…

Optimization and Control · Mathematics 2023-01-09 Suyun Liu , Luis Nunes Vicente

We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…

Optimization and Control · Mathematics 2020-11-20 Kimon Antonakopoulos , E. Veronica Belmega , Panayotis Mertikopoulos

We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…

Optimization and Control · Mathematics 2024-10-07 Aleksandr Beznosikov , Darina Dvinskikh , Dmitry Bylinkin , Andrei Semenov , Alexander Gasnikov

We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…

Optimization and Control · Mathematics 2017-10-19 Achintya Kundu , Francis Bach , Chiranjib Bhattacharyya

We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…

Numerical Analysis · Mathematics 2018-06-05 Robert Plato , Bernd Hofmann

Most existing results about \emph{last-iterate convergence} of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results…

Computer Science and Game Theory · Computer Science 2022-03-24 Ioannis Anagnostides , Ioannis Panageas , Gabriele Farina , Tuomas Sandholm

In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an…

Optimization and Control · Mathematics 2021-06-30 Xin He , Rong Hu , Ya-Ping Fang