Development and analysis of numerical methods and software for scientific computing. Recent research topics:

• first- and second-order methods for deterministic and stochastic nonlinear optimization (gradient, split-Bregman, quasi-Newton, interior point), with applications to image processing and machine learning;

• preconditioners for large and sparse linear systems arising in optimization problems (constraint preconditioners for saddle-point systems, preconditioner updates, matrix-free preconditioners);

• parallel algebraic multilevel preconditioners with applications to sparse linear systems arising in fluid dynamics simulations on HPC computers.