Otimização global topográfica para solução de sistemas de equações não lineares restritos e aplicações à estabilidade de fases de misturas termodinâmicas

• Autor(a) principal: Costa, Janaina Imbiriba da
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13830
• topic: Topographical optimization; Systems of equations; Stability analysis; Otimização topográfica; Sistemas de equações; Análise de estabilidade; Otimização matemática; Sistemas não-lineares; Diagrama de fases Termodinâmica; Métodos de simulação; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

Optimization methods that use optimality conditions of first and/or second order are known to be efficient. Commonly, such iterative methods are developed and analyzed in the light of knowledge concerning the mathematical analysis in n-dimensional Euclidean spaces, whose nature is of local character. Consequently, these methods lead to iterative algorithms that perform only local searches. Thus, the application of such algorithms to the calculation of global minimizers of a non-linear function, especially non-convex and multimodal, depends strongly on the location of the starting points. The Topographical Global Optimization method is a clustering algorithm, which uses an ingenious approach based on elementary concepts of graph theory, in order to generate good starting points for local search methods, from points distributed uniformly in the interior of the feasible set. In this work, we apply a recently revisited version of the topographical global initialization to solve nonlinear systems of equations with multiple roots subject to inequality constraints. In addition, to accomplish the tasks of local search in feasible sets, we use an interior-point method. Our methodology was compared against other methods using benchmarks from the literature, and the results indicated that the present approach is a powerful strategy for find all roots of nonlinear systems. Then, it was made is application of this method to the phase stability analysis of mixtures, a difficult and important global optimization problem of the chemical engineering.