Inicialização Global Topográfica aplicada a problemas de autovalores e de otimização com restrições mistas

Abstract

The classical mathematical methods, developed from the Rn analysis, have widely been usedin the solution of different problems in mathematics, physics and engineering. In general, these methods perform a local search based on an initial estimate. This fact can present great difficulties, because in many cases, adequate starting points are not available in the formulation of the problems. In this context, the Global Topographic Initialization is an efficient method for selecting suitable initial estimates. For this, the method makes use of graph theory concepts to refine a set of sample points uniformly generated in the feasible set. However, there are cases in which the closest sample point to a solution is not selected due to the fact that one of its nearest neighbors is in a small valley. To overcome this difficulty, in the present work we propose a modification in the selection process of the initial estimates. Such modification also allows, in certain cases, the use of fewer sample points. Using the Modified Topographic Global Initialization we solve the eigenvalues problem of real symmetric matrices, complementary eigenvalues and minimization with equality and inequality constraints. In order to test the Modified Topographic Global Initialization performance in selection of initial estimates for the local search methods, we have carried out computational experiments using problems described in the literature. In all tests, including those with several solutions, the methodology presented here proved to be robust in calculating the solutions.