A gradient descent algorithm built on approximate discrete gradients

Abstract

We propose an optimization method obtained by the approximation of a novel discretization approach for gradient dynamics recently proposed by the authors. It is shown that the proposed algorithm ensures convergence for all amplitudes of the step size, contrarily to classical implementations.

Passivity Techniques and Hamiltonian Structures in Discrete Time

“…Specifying the result in Theorem 4 to port-Hamiltonian structures, one gets preservation of the port-Hamiltonian structure under power-preserving interconnection; a qualifying property to discuss energy management based control schemes. Examples in this direction are developed in [41,43,42,22,23,38].…”