Métodos Quasi-Newton Proximais para Problemas de Otimização Composta

Abstract

In this work, we analyze the proximal quasi-Newton method and its accelerated version to solve composite optimization problems. The study of the non-accelerated version is based on the reference [17], while the accelerated version is based on [3]. It is shown that the classical method obtains a convergence rate of O(1/k), i.e., for a given precision ε > 0, the method generates an iteration xk such that F (xk) − F (x∗) < ε in at most O(1/ε) iterations, where x∗ is a global minimizer of the problem mentioned above. For the accelerated version we obtain a better convergence rate of O(1/k2).