Activities in this area at IMPA began in the 1970’s with the group at the time referred to as Operational Research. Nowadays, the research focus of the group is concentrated on continual optimization and correlated areas.
Among specific topics of this research, we would like to mention:
- Iterative methods for convex optimization or convex viability on a grand scale, with applications in image reconstruction from projections (e.g., computerized tomography)
- Computational methods for non-linear complementarity problems and variational inequalities
- Algorithms of parallel optimization
- Generalizations of proximal point method for convex optimization and variational inequalities (including recent non convex and non monotone cases)
- New approaches to duality in non linear programming
- Non monotone methods for non linear optimization
Three new themes have been added recently: new theories of regularity in finite dimension (particularly, regularity-2), extensions of maximal monotone operators, generalizing the є-convex subdifferential function, and Banach space optimization.