The proximal point method with a vectorial Bregman regularization in multiobjective DC programming. (2nd January 2022) - Souza, João Carlos de O.; Cruz Neto, João Xavier da; Lopes, Jurandir de Oliveira; Silva, Roberto Cristóvão Mesquita; Bitar, Sandro Dimy Barbosa
Abstract : For solving constrained multiobjective problems with a vector-valued DC (difference of convex) objective function, we consider a vectorial Bregman regularized proximal point method which extends both the scalar proximal point method for DC functions and the vectorial proximal point method for vector-valued convex functions. By using a vectorial regularization function, our method does not use auxiliary vectorial sequences to make the method a vectorial one but providing an extra flexibility to the method. Some encouraging numerical experiments are presented.