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Non-linear least squares and global optimization

Grant number: 11/22242-0
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): April 01, 2012
Effective date (End): September 30, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:José Mário Martinez Perez
Grantee:Hector Flores Callisaya
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Many practical problems in physics, engineering, economics and other sciences are modeled in a very convenient way by a nonlinear system indeterminate. It is usual in such cases, that some modern version of Newton's method, is used successfully. However, the method is iterative and local in the sense that we can only guarantee convergence to a solution assuming that the starting point used as an approximation of it is already good enough. But in practice, building good initial points is not an easy task, so the need to seek equivalent mathematical models. The nonlinear system can be written as a global optimization problem, however, there isn't an exact method for solving local or global optimization, which makes it really difficult to solve this problem. Have been published, good algorithms and heuristics that guarantee convergence to the global minimizer with a certain probability. Based in good numerical results obtained in the doctoral dissertation of the candidate, the proposal is to more detailed study on methods of global optimization problems for nonlinear least squares, using the structure of the problem.