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This paper deals with a second-order primal-dual dynamical system with Hessian-driven damping and Tikhonov regularization terms in connection with a convex-concave bilinear saddle point problem. We first obtain a fast convergence rate of…

Optimization and Control · Mathematics 2026-02-27 Xiangkai Sun , Liang He , Xianjun Long

In this paper, we propose a general Tikhonov regularized second-order dynamical system with viscous damping, time scaling and extrapolation coefficients for the convex-concave bilinear saddle point problem. By the Lyapunov function…

Optimization and Control · Mathematics 2026-02-02 Bohan Zhang , Xiaojun Zhang

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 a Hilbert framework, we consider an inertial Tikhonov regularized dynamical system governed by a maximally comonotone operator, where the damping coefficient is proportional to the square root of the Tikhonov regularization parameter.…

Optimization and Control · Mathematics 2024-12-02 Zeng-Zhen Tan , Rong HU , Ya-Ping Fang

In a Hilbert framework, for convex differentiable optimization, we consider accelerated gradient methods obtained by combining temporal scaling and averaging techniques with Tikhonov regularization. We start from the continuous steepest…

Optimization and Control · Mathematics 2022-11-21 Hedy Attouch , Zaki Chbani , Hassan Riahi

In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of…

Optimization and Control · Mathematics 2020-08-31 Radu Ioan Boţ , Sorin-Mihai Grad , Dennis Meier , Mathias Staudigl

We consider the minimization of a convex objective function subject to the set of minima of another convex function, under the assumption that both functions are twice continuously differentiable. We approach this optimization problem from…

Optimization and Control · Mathematics 2016-08-16 Radu Ioan Bot , Ernö Robert Csetnek

This paper deals with an inertial proximal algorithm that contains a Tikhonov regularization term, in connection to the minimization problem of a convex lower semicontinuous function $f$. We show that for appropriate Tikhonov regularization…

Optimization and Control · Mathematics 2024-01-09 Szilárd Csaba László

In a Hilbert space, we propose a class of general mixed-order primal-dual dynamical systems with Tikhonov regularization for a convex optimization problem with linear equality constraints. The proposed dynamical system is characterized by…

Optimization and Control · Mathematics 2025-07-31 Honglu Li , Rong Hu , Xin He , Yibin Xiao

We investigate the strong convergence properties of a Nesterov type algorithm with two Tikhonov regularization terms in connection to the minimization problem of a smooth convex function $f.$ We show that the generated sequences converge…

Optimization and Control · Mathematics 2023-08-10 Mikhail Karapetyants , Szilárd Csaba László

In this paper, we study an explicit Tikhonov-regularized inertial gradient algorithm for smooth convex minimization with Lipschitz continuous gradient. The method is derived via an explicit time discretization of a damped inertial system…

Optimization and Control · Mathematics 2026-02-02 Samir Adly , Vinh Thanh Ho , Huu Nhan Nguyen

This paper deals with a Tikhonov regularized second-order plus first-order primal-dual dynamical system with time scaling for separable convex optimization problems with linear equality constraints. This system consists of two second-order…

Optimization and Control · Mathematics 2025-10-29 Xiangkai Sun , Lijuan Zheng , Kok Lay Teo

This work is concerned with linear inverse problems where a distributed parameter is known a priori to only take on values from a given discrete set. This property can be promoted in Tikhonov regularization with the aid of a suitable convex…

Optimization and Control · Mathematics 2018-04-19 Christian Clason , Thi Bich Tram Do

We investigate the asymptotic behavior of solutions to a second order differential equation with vanishing damping term, convex potential and regularizing Tikhonov term.

Optimization and Control · Mathematics 2017-12-01 Mounir Elloumi , Ramzi May , Chokri Mnasri

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system of proximal-gradient type stated in connection with the minimization of the sum of a nonsmooth convex and a (possibly nonconvex)…

Optimization and Control · Mathematics 2017-11-20 Radu Ioan Bot , Ernö Robert Csetnek , Szilárd Csaba László

We investigate the strong convergence properties of a proximal-gradient inertial algorithm with two Tikhonov regularization terms in connection to the minimization problem of the sum of a convex lower semi-continuous function $f$ and a…

Optimization and Control · Mathematics 2024-07-16 Szilárd Csaba László

In this paper, we propose a Tikhonov-like regularization for dynamical systems associated with non-expansive operators defined in closed and convex sets of a Hilbert space. We prove the well-posedness and the strong convergence of the…

Optimization and Control · Mathematics 2020-07-23 Pedro Pérez-Aros , Emilio Vilches

In a real Hilbert space setting, we investigate the asymptotic behavior of the solutions of the classical Arrow-Hurwicz differential system combined with Tikhonov regularizing terms. Under some newly proposed conditions on the Tikhonov…

Optimization and Control · Mathematics 2025-09-03 Fouad Battahi , Zaki Chbani , Simon K. Niederländer , Hassan Riahi

In this paper we study a second order dynamical system with variable coefficients in connection to the minimization problem of a smooth nonconvex function. The convergence of the trajectories generated by the dynamical system to a critical…

Optimization and Control · Mathematics 2025-10-21 Szilárd Csaba László

In this paper we deal with a general second order continuous dynamical system associated to a convex minimization problem with a Fr\`echet differentiable objective function. We show that inertial algorithms, such as Nesterov's algorithm,…

Optimization and Control · Mathematics 2019-08-08 Cristian Daniel Alecsa , Szilárd Csaba László , Titus Pinţa