Métodos poliedro-elipsoidais para problemas de otimização contínuos ediscretos quasi-convexos

Abstract

This Thesis proposal will introduce a new class of methods that belongs to the Semi-Space Excluding class and are based on Ellipsoidal algorithm. This new methods' class is playable for solving real, integer or mixed integer variables problems with single or vector cost functions in which all functions can be quasi-convex non necessarily differentiable. This new methods' class is here called Polyhedron-Ellipsoid class. When this new methods' class is applied on real variables problems, the convergence speed-up is supported by using KTE cones for compressing the search region, assembled from current or already calculated information. When this new methods' class is applied on integer or mixed integer variables problems the global convergence is guaranteed by an implicit or explicit enumeration function together with the Ellipsoid algorithm. For these integer or mixed integer problems the convergence speed-up is supported by a Branch-and-Cut algorithm. Computational tests, for single-objective problems, will exhibit a significant improve in convergence performance parameters as calculation time, volume reduction tax and number of objective-function calls. The results point to enhanced ones whether the problem evaluation effort increases. The proposed methods' class will also prove to be useful for finding, efficiently, non-dominated points in vector-objective problems as well for demonstrating that a problem is feasible or not.