Related papers: Inertial Methods with Viscous and Hessian driven D…
In a Hilbert setting, we develop fast methods for convex unconstrained optimization. We rely on the asymptotic behavior of an inertial system combining geometric damping with temporal scaling. The convex function to minimize enters the…
Our approach is part of the close link between continuous dissipative dynamical systems and optimization algorithms. We aim to solve convex minimization problems by means of stochastic inertial differential equations which are driven by the…
Second-order continuous-time dissipative dynamical systems with viscous and Hessian driven damping have inspired effective first-order algorithms for solving convex optimization problems. While preserving the fast convergence properties of…
In a Hilbert space setting, for convex optimization, we show the convergence of the iterates to optimal solutions for a class of accelerated first-order algorithms. They can be interpreted as discrete temporal versions of an inertial…
This paper is devoted to the investigation of inertial dynamical systems with implicit Hessian-driven damping for strongly quasiconvex optimization which is a specific class of nonconvex optimization problems. We first establish exponential…
In a Hilbert space setting, for convex optimization, we analyze the convergence rate of a class of first-order algorithms involving inertial features. They can be interpreted as discrete time versions of inertial dynamics involving both…
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…
This paper deals with a second order dynamical system with a Tikhonov regularization term in connection to the minimization problem of a convex Fr\'echet differentiable function. The fact that beside the asymptotically vanishing damping we…
In this work, we investigate a second-order dynamical system with Hessian-driven damping tailored for a class of nonconvex functions called strongly quasiconvex. Buil\-ding upon this continuous-time model, we derive two discrete-time…
In a Hilbert setting we study the convergence properties of a second order in time dynamical system combining viscous and Hessian-driven damping with time scaling in relation with the minimization of a nonsmooth and convex function. The…
This paper deals with a Tikhonov regularized second-order inertial dynamical system that incorporates time scaling, asymptotically vanishing damping and Hessian-driven damping for solving convex optimization problems. Under appropriate…
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…
The Hessian-vector product has been utilized to find a second-order stationary solution with strong complexity guarantee (e.g., almost linear time complexity in the problem's dimensionality). In this paper, we propose to further reduce the…
In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can…
In a Hilbert space $H$, in order to develop fast optimization methods, we analyze the asymptotic behavior, as time $t$ tends to infinity, of inertial continuous dynamics where the damping acts as a closed-loop control. The function $f: H…
We first study the fast minimization properties of the trajectories of the second-order evolution equation $$\ddot{x}(t) + \frac{\alpha}{t} \dot{x}(t) + \beta \nabla^2 \Phi (x(t))\dot{x} (t) + \nabla \Phi (x(t)) = 0,$$ where $\Phi:\mathcal…
We study the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system combining asymptotic vanishing viscous and Hessian-driven damping. We establish a fast sublinear convergence…
In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics where the coefficients are designed in a closed-loop way.…
In this paper, we examine the convergence properties of heavy-ball dynamics with Hessian-driven damping in smooth non-convex optimization problems satisfying a {\L}ojasiewicz condition. In this general setting, we provide a series of tight,…
In a Hilbert setting we aim to study a second order in time differential equation, combining viscous and Hessian-driven damping, containing a time scaling parameter function and a Tikhonov regularization term. The dynamical system is…