inertial proximal algorithm – Optimization Online

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

Published: 2014/10/02

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

An inertial Tseng’s type proximal algorithm for nonsmooth and nonconvex optimization problems

Published: 2014/06/03

Radu Ioan Bot

Ernö Robert Csetnek

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

We investigate the convergence of a forward-backward-forward proximal-type algorithm with inertial and memory effects when minimizing the sum of a nonsmooth function with a smooth one in the absence of convexity. The convergence is obtained provided an appropriate regularization of the objective satisfies the Kurdyka-\L{}ojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. Article … Read more