In the framework of real Hilbert spaces, we study continuous in time dynamics as well as
numerical algorithms for the problem of approaching the set of zeros of a single-valued …

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 …

We analyze continuous-time models of accelerated gradient methods through deriving
conservation laws in dilated coordinate systems. Namely, instead of analyzing the dynamics …

We revisit the Ravine method of Gelfand and Tsetlin from a dynamical system perspective,
study its convergence properties, and highlight its similarities and differences with the …

In this paper, we propose an accelerated variant of the proximal point algorithm for
computing a zero of an arbitrary maximally monotone operator A. The method incorporates …

We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a
convex function in a finite-dimensional Euclidean space. Given a function\varPhi: R^ d → R …

Second-order continuous-time dissipative dynamical systems with viscous and Hessian
driven damping have inspired effective first-order algorithms for solving convex optimization …

This paper deals with a second order dynamical system with vanishing damping that
contains a Tikhonov regularization term, in connection to the minimization problem of a …

The aim of this survey is to present the main important techniques and tools from variational
analysis used for first and second order dynamical systems of implicit type for solving …

This paper examines a perturbed heavy ball system with vanishing damping that contains a
Tikhonov regularization term in connection to the minimization problem of a convex Fréchet …