A modified proximal point method for DC functions on Hadamard manifolds

• DOI: 10.1007/s10589-020-00173-3
• Publication Date: 2020-02-08T19:02:16Z
• Authors: Yldenilson Torres...; João Xavier da Cr...; Paulo Roberto Oli...; João Carlos de Ol...
• Keywords: 0101 mathematics; 01 natural sciences

We study the convergence of a modified proximal point method for DC functions in Hadamard manifolds. We use the iteration computed by the proximal point method for DC function extended to the Riemannian context by Souza and Oliveira (J Glob Optim 63:797–810, 2015) to define a descent direction which improves the convergence of the method. Our method also accelerates the classical proximal point method for convex functions. We illustrate our results with some numerical experiments.