A Time-certified Predictor-corrector IPM Algorithm for Box-QP
Liang Wu, Yunhong Che, Richard D. Braatz, Jan Drgona
TL;DR
The paper tackles time-certified optimization for Box-QP in real-time MPC by introducing a feasible predictor-corrector interior-point method that preserves an $O(\sqrt{n})$ worst-case iteration bound while delivering strong practical performance. It leverages a cost-free initialization and a reduced Newton system to compute predictor and corrector directions, ensuring iterates remain within a central neighborhood. The method achieves a 5x speedup over the authors' previous time-certified IPM and exhibits practical iteration counts of $O(\log n)$ or $O(n^{0.25})$ in experiments, including a nonlinear PDE-MPC case. This work enhances real-time applicability of IPM-based QP solvers by providing data-independent guarantees and accessible code, though per-iteration cost is higher due to solving two linear systems.
Abstract
Minimizing both the worst-case and average execution times of optimization algorithms is equally critical in real-time optimization-based control applications such as model predictive control (MPC). Most MPC solvers have to trade off between certified worst-case and practical average execution times. For example, our previous work [1] proposed a full-Newton path-following interior-point method (IPM) with data-independent, simple-calculated, and exact $O(\sqrt{n})$ iteration complexity, but not as efficient as the heuristic Mehrotra predictor-corrector IPM algorithm (which sacrifices global convergence). This letter proposes a new predictor-corrector IPM algorithm that preserves the same certified $O(\sqrt{n})$ iteration complexity while achieving a $5\times$ speedup over [1]. Numerical experiments and codes that validate these results are provided.