Metodo de direções interiores ao epígrafo - IED para otimização não diferenciável e não convexa via Dualidade Lagrangeana: estratégias para minimização da Lagrangeana aumentada

Abstract

The classical theory of optimization assumes the existence of certain conditions, for example, that the functions involved in a problem of this nature are at least once continuously differentiable. However, in many practical applications that require the use of optimization methods, this characteristic is not present. Non-differentiable optimization problems are considered more difficult to deal with. In this class, those involving nonconvex functions are even more complex. Interior Epigraph Directions (IED) is an optimization method that is based on Lagrangean duality theory and applies to the resolution of non-differentiable, non-convex and constrained problems. In this study, we present two new versions for this method from computational implementations of other algorithms. The first version, called IED + NFDNA, received the incorporation of an implementation of the Nonsmooth Feasible Direction Nonconvex Algorithm (NFDNA) algorithm. This version, when applied in numerical experiments with problems in the literature, presented satisfactory performance when compared to the original IED and other optimization solvers. A second version, IED + GA, was developed with the use of genetic algorithms in order to further refine the method, reducing its dependence on initial parameters and also on the calculation of subgradients. In addition to solving test problems, IED + GA achieved good results when applied to engineering problems.