Computational methods in optimization

Abstract

Our group has been active in the Brazilian scientific environment for 40 years, being is sensitive to new trends and modern applications of Optimization. Over the years, this group, funded by successive FAPESP thematic projects, has made significant contributions in areas involving decomposition methods, quasi-Newton methods, sequential quadratic programming, augmented Lagrangian methods, inexact restoration, large scale problems, sequential optimality conditions, derivative-free optimization, algorithmic complexity, image reconstruction and machine learning, among others. The experience accumulated along the years, as well as the incorporation and renewal of the research team, enable us to tackle problems in which the objective function is difficult, impossible to evaluate, or of questionable existence; the number of variables is enormous or unknown, and finally, the uncertainty extends to the constraints. Addressing these problems necessarily requires interdisciplinary approaches and the desired impact is at the same time scientific, economic and social. (AU)