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A new equivalent reformulation of the absolute value equations associated with second-order cone (SOCAVEs) is emphasised, from which a dynamical system based on projection operator for solving SOCAVEs is constructed. Under proper…

Dynamical Systems · Mathematics 2022-08-11 Cairong Chen , Dongmei Yu , Deren Han , Changfeng Ma

For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…

Optimization and Control · Mathematics 2026-03-25 Geng-Hua Li , Hai-Yi Zhao , Xiangkai Sun

In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…

Functional Analysis · Mathematics 2014-05-22 Ibrahim Karahan , Murat Ozdemir

In this paper, we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and…

Optimization and Control · Mathematics 2025-06-30 Radu Ioan Bot , Konstantin Sonntag

Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…

Optimization and Control · Mathematics 2023-07-11 Adarsh Barik , Suvrit Sra , Jean Honorio

This paper is devoted to the study of an inertial accelerated primal-dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality…

Optimization and Control · Mathematics 2026-04-30 Huan Zhang , Xiangkai Sun , Shengjie Li , Kok Lay Teo

This paper investigates zeroth-order (ZO) finite-sum composite optimization. Recently, variance reduction techniques have been applied to ZO methods to mitigate the non-vanishing variance of 2-point estimators in constrained/composite…

Optimization and Control · Mathematics 2026-01-09 Silan Zhang , Yujie Tang

The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint…

Optimization and Control · Mathematics 2024-06-24 R. Díaz Millán , O. P. Ferreira , J. Ugon

In this work, we present new simple and optimal algorithms for solving the variational inequality (VI) problem for $p^{th}$-order smooth, monotone operators -- a problem that generalizes convex optimization and saddle-point problems. Recent…

Optimization and Control · Mathematics 2022-06-01 Deeksha Adil , Brian Bullins , Arun Jambulapati , Sushant Sachdeva

We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of…

Machine Learning · Statistics 2023-12-08 Nicolas Zilberstein , Ashutosh Sabharwal , Santiago Segarra

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

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…

Optimization and Control · Mathematics 2021-01-25 Yekini Shehu , Olaniyi. S. Iyiola , Xiao-Huan Li , Qiao-Li Dong

Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…

Optimization and Control · Mathematics 2020-11-23 Tristan van Leeuwen , Aleksandr Aravkin

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

In this technical note, we are concerned with the problem of solving variational inequalities with improved convergence rates. Motivated by Nesterov's accelerated gradient method for convex optimization, we propose a Nesterov's accelerated…

Optimization and Control · Mathematics 2022-12-21 Shaolin Tan , Jinhu Lu

In this paper we present a new method for solving optimization problems involving the sum of two proper, convex, lower semicontinuous functions, one of which has Lipschitz continuous gradient. The proposed method has a hybrid nature that…

Optimization and Control · Mathematics 2022-11-03 Kristian Bredies , Enis Chenchene , Alireza Hosseini

We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…

Machine Learning · Computer Science 2023-12-06 Benjamin J. Holzschuh , Simona Vegetti , Nils Thuerey

The paper starts with a concise description of the recently developed semismooth* Newton method for the solution of general inclusions. This method is then applied to a class of variational inequalities of the second kind. As a result, one…

Optimization and Control · Mathematics 2020-07-23 Helmut Gfrerer , Jiri V. Outrata , Jan Valdman

We introduce an inexact oracle model for variational inequalities (VI) with monotone operator, propose a numerical method which solves such VI's and analyze its convergence rate. As a particular case, we consider VI's with…

Optimization and Control · Mathematics 2022-02-18 Fedor Stonyakin , Alexander Gasnikov , Pavel Dvurechensky , Mohammad Alkousa , Alexander Titov

Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting. We aim to study stochastic convex minimization problems through the…

Optimization and Control · Mathematics 2025-02-21 Rodrigo Maulen-Soto , Jalal Fadili , Hedy Attouch , Peter Ochs