Speaker
Description
Nonlinear model predictive control schemes solving the step-wise local optimization problems via, e.g. ipopt lead to the necessity to solve large KKT systems in each step of the optimizer. The KKT system itself is a saddle point matrix and, due to the outer MPC approach, ideally has Kronecker structure.
Ipopt uses the matrix inertia of the KKT system to accelerate computations. Classic LU-based solvers use the matrix factorization to derive the inertia as a side product. Due to the Kronecker structure, we want to use structured linear algebra solvers tackling Sylvester-type equations rather than the LU of the large Kronecker matrix. For optimal performance of ipopt, this, however, requires a way to compute or estimate the inertia of the Kronecker matrix from the small block data.
