Optimización no suave a través de métodos de Tipo Newton : Optimización no suave a través de métodos BFGS y L-BFGS.

Abstract

This paper is concerned about the study of unconstrained and non-smooth optimization problems through the formulation of this problem by the Forward - Backward Envelope (FBE), function that provides an interpretation for the Forward-Backward Splitting (FBS) as a gradient method. Subsequently, an FBS - type algorithm is constructed, which recognizes the strong properties of convexity and complexity of this type of methods, along the decomposition of a non-smooth function by the Forward - Backward Envelope. We look for a superlinear convergence of the method by preconditioning the gradient with BFGS. Finally, we implement the algorithm in MATLAB language and a Bingham Problem is used as an example to evaluate the code.