pdaqp 0.2.0

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.

Installation

pip install pdaqp

Example

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

import pdaqp
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()