The group is dedicated to the analysis from the theoretical point of view (existence, uniqueness, regularity, stability and asymptotic behavior of solutions) and also from the numerical point of view (approximate solutions, convergence and error evaluation) of continuous optimization and optimal control problems. The problems to be addressed include L-infinite ergodic problems, variational inequalities in finite dimensions and Banach spaces, projected dynamical systems and variational inclusions. The methodology is based in the application and extension of techniques such as dynamic programming, the equation of Hamilton-Jacobi-Bellmann, solutions in the viscosity sense, Pontryagin maximum principle, proximal methods, decomposition methods, finite element approaches, descent methods and fixed point theorems for nonlinear operators.
In our approach, the development of efficient algorithms and their implementation in specific applications such as traffic problems impacting in transport networks, the coordination of hydrothermal problems in systems for the generation and transmission of electricity, image reconstruction problems from incomplete information and the optimization of multi-production machines.
The training young professionals through the supervision of undergraduate projects and doctoral thesis is also a priority of our work.