Otimização global usando trajetorias densas e aplicações

Abstract

In this work a new global optimization method is defined combining deterministic and stochastic ideas. For this, we use a strategy to escape of local minimums established in following the trajectory of the Lissajous curve, a dense and smooth curve in an limited box Ω.The global algorithm is applied in a geophysical problem, known as the Common Reflection Surface (CRS) problem, and in the problem to find hidden patterns.Also we present a quasi-Newton method for the OVO problem that generalizes the Cauchy local method (used here as local method to find hidden patterns), and prove its superlinear and quadratic convergence. This new method is applied to a Brazilian variation of the Stiglitz's Ideal Banking System.