PIQP: A Proximal Interior-Point Quadratic Programming Solver
Abstract
This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle ill-conditioned convex QP problems without the need for linear independence of the constraints. The open-source implementation is written in C++ with interfaces to C, Python, Matlab, and R leveraging the Eigen3 library. The method uses a pivoting-free factorization routine and allocation-free updates of the problem data, making the solver suitable for embedded applications. The solver is evaluated on the Maros-Mészáros problem set and optimal control problems, demonstrating state-of-the-art performance for both small and large-scale problems, outperforming commercial and open-source solvers.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2023
- DOI:
- 10.48550/arXiv.2304.00290
- arXiv:
- arXiv:2304.00290
- Bibcode:
- 2023arXiv230400290S
- Keywords:
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- Mathematics - Optimization and Control