Szilard Csaba Laszlo – Optimization Online

A second order dynamical approach with variable damping to nonconvex smooth minimization

Published: 2018/05/07

Nonsmooth Optimization convergence rate, kurdyka-lojasiewicz inequality, nonconvex optimization, second order dynamical system

We investigate a second order dynamical system with variable damping in connection with the minimization of a nonconvex differentiable function. The dynamical system is formulated in the spirit of the differential equation which models Nesterov’s accelerated convex gradient method. We show that the generated trajectory converges to a critical point, if a regularization of the … Read more

An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions

Published: 2014/10/02

Radu Ioan Bot

Ernö Robert Csetnek

Szilard Csaba Laszlo

Nonsmooth Optimization bregman distance, inertial proximal algorithm, kurdyka-lojasiewicz inequality, limiting subdifferential, nonsmooth optimization

We propose a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. The sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Lojasiewicz inequality, which is … Read more