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Numerical Optimization

Abstract

This project deals with theoretical, computational and application aspects of Optimization. The project aims at the development, theoretical analysis, implementation and application of algorithms for different aspects of Optimization, with emphasis on Continuous Optimization. The project relies on applications with which the team is familiar. Emphasis is placed on algorithms with a solid theoretical background, which involves precise characterization of the problems addressed, with careful and competitive computational implementation, and connections to Engineering and Applied Sciences. The project team has been active in the Brazilian scientific environment for over 40 years, and is sensitive to new trends and modern applications of Optimization. Over the years, the team has made significant contributions in areas involving decomposition methods, quasi-Newton methods, sequential quadratic programming, Augmented Lagrangian methods, Inexact Restoration, large problems, sequential optimality conditions, derivative-free minimization, algorithmic complexity, image reconstruction and machine learning, among others. The experience accumulated, as well as the incorporation and renewal of the research team in the project, enables the team 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 scientific, economic, and social at the same time. (AU)

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