Jingtao Xiong

Monday, November 30, 2026, 11:00

Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany

In nonlinear model predictive control (NMPC), sequential quadratic programming
(SQP) with the exact Hessian of the Lagrangian produces quadratic program (QP)
subproblems of which the full Hessian can be indefinite. Structure-exploiting QP
solvers embedded in the SQP solver often require a positive definite full Hessian,
so the full Hessian is regularized at the SQP level before it is passed to the solver,
which in general changes the solution of each QP and also the feedback in SQP
with real-time iteration. In contrast to SQP-level regularizations, regularizing at
the QP level can introduce two advantages. First, this lets the solver exploit the
curvature from inequality constraints without extra estimation, and, second, only
return the solution of the original QP.
This thesis investigates primal regularizations inside interior-point solvers for
indefinite QPs with optimal control problem (OCP) structure, with a focus on the
proposed Riccati-based regularization, which regularizes only at the stages where
the Cholesky factorization fails during Riccati recursion. This thesis shows with a
general case that the minimum perturbation strategy can make the Riccati-based
regularization fail, and further derives an improved strategy from the case to avoid
such failure. It is proven that the Riccati-based regularization becomes inactive
near the solution.
For evaluation, this thesis builds a benchmark of 175 indefinite OCP QPs from
the SQP iterations. With the regularizations implemented in a prototype solver
that reproduces the iterations of HPIPM on convex QPs, This thesis compares the
Riccati-based regularization with full Hessian regularization and inertia correction
in terms of robustness, efficiency and estimated factorization cost.