pdaqp 0.5.1

A multi-parametric quadratic programming solver

pdaqp is a Python package for solving multi-parametric quadratic programs of the form

$$ \begin{align} \min_{z} & ~\frac{1}{2}z^{T}Hz+(f+F \theta)^{T}z \ \text{s.t.} & ~A z \leq b + B \theta \ & ~\theta \in \Theta \end{align} $$

where $H \succ 0$ and $\Theta \triangleq \lbrace l \leq \theta \leq u : A_{\theta} \theta \leq b_{\theta}\rbrace$.

pdaqp is based on the Julia package ParametricDAQP.jl and the Python module juliacall. More information about the underlying algorithm and numerical experiments can be found in the paper "A High-Performant Multi-Parametric Quadratic Programming Solver".

Installation

pip install pdaqp

Citation

If you use the package in your work, consider citing the following paper

@inproceedings{arnstrom2024pdaqp,
  author={Arnström, Daniel and Axehill, Daniel},
  booktitle={2024 IEEE 63rd Conference on Decision and Control (CDC)}, 
  title={A High-Performant Multi-Parametric Quadratic Programming Solver}, 
  year={2024},
  volume={},
  number={},
  pages={303-308},
}

Example

The following code solves the mpQP in Section 7.1 in Bemporad et al. 2002

import numpy

H =  numpy.array([[1.5064, 0.4838], [0.4838, 1.5258]])
f = numpy.zeros((2,1))
F = numpy.array([[9.6652, 5.2115], [7.0732, -7.0879]])
A = numpy.array([[1.0, 0], [-1, 0], [0, 1], [0, -1]])
b = 2*numpy.ones((4,1));
B = numpy.zeros((4,2));

thmin = -1.5*numpy.ones(2)
thmax = 1.5*numpy.ones(2)

from pdaqp import MPQP
mpQP = MPQP(H,f,F,A,b,B,thmin,thmax)
mpQP.solve()

To construct a binary search tree for point location, and to generate corresponding C-code, run

mpQP.codegen(dir="codegen", fname="pointlocation")

which will create the following directory:

├── codegen
│   ├── pointlocation.c
│   └── pointlocation.h

The critical regions and the optimal solution can be plotted with the commands

mpQP.plot_regions()
mpQP.plot_solution()

which create the following plots