Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems
AbstractThe present work deals with the numerical long-time integration of damped Hamiltonian systems. The method that we analyze combines a…
Optimization
The long time behavior and the rate of convergence of symplectic convex algorithms obtained via splitting discretizations of inertial damping systems
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AbstractIn this paper we propose new numerical algorithms in the setting of unconstrained optimization problems and we give proof for…
An extension of the second order dynamical system that models Nesterov’s convex gradient method
Abstract In this paper we deal with a general second order continuous dynamical system associated to a convex minimization problem…
New optimization algorithms for neural network training using operator splitting techniques
AbstractWe present a new type of optimization algorithms, adapted for neural network training. These algorithms are based upon sequential operator…
A gradient-type algorithm with backward inertial steps associated to a nonconvex minimization problem
AbstractWe investigate an algorithm of gradient type with a backward inertial step in connection with the minimization of a nonconvex…
Publications
Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media
AbstractFlow and multicomponent reactive transport in saturated/unsaturated porous media are modeled by ensembles of computational particles moving on regular lattices according to specific random walk rules. The occupation number of…
Read More Functional differential equations with maxima, via step by step contraction principle
AbstractT. A. Burton presented in some examples of integral equations a notion of progressive contractions on C([a, ∞[). In 2019, I. A. Rus formalized this notion (I. A. Rus, Some…
Read More How many steps still left to x*?
Emil Cătinaş
Abstract The high speed of \(x_{k}\rightarrow x^\ast\in{\mathbb R}\) is usually measured using the C-, Q- or R-orders: \begin{equation}\tag{$C$} \lim \frac {|x^\ast – x_{k+1}|}{|x^\ast – x_k|^{p_0}}\in(0,+\infty), \end{equation} \begin{equation}\tag{$Q$} \lim \frac {\ln…
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