darnstrom / daqp

A dual active-set algorithm for convex quadratic programming

DAQP

DAQP is a dual active-set solver that solves convex quadratic programs of the form

minimize        0.5 x' H x + f' x

subject to      l  <=  x  <= u
		bl <=  Ax <= bu.

Binary constraints of the form $A x \in \lbrace b_l, b_u \rbrace$ are also supported, allowing for mixed-integer quadratic programs to be solved.

The code is written in C and is library free. DAQP can be interfaced to C, Julia, MATLAB, and Python.

Quick installation

Julia

] add DAQP

MATLAB

websave('install_daqp','https://raw.githubusercontent.com/darnstrom/daqp/master/interfaces/daqp-matlab/install_daqp.m')
install_daqp

Python

pip install daqp

Details

See the Documentation for more detailed installation instructions and basic use of the interfaces.

Citing DAQP

@article{arnstrom2022dual,
  author={Arnström, Daniel and Bemporad, Alberto and Axehill, Daniel},
  journal={IEEE Transactions on Automatic Control},
  title={A Dual Active-Set Solver for Embedded Quadratic Programming Using Recursive {LDL}$^{T}$ Updates},
  year={2022},
  volume={67},
  number={8},
  pages={4362-4369},
  doi={10.1109/TAC.2022.3176430}
}

daqp's Issues

Add const

In the API, correctly use const for some of the arguments

Add example in documentation about how to warm/hot-start in C

Update example in documentation to be more informative

For example, use an example that that highlight that matrices are row major.

Warmstart

Dear Darnstrom,

thank you for sharing this wonderful lightweight QP solver. After a few tests, this solver seems to be the perfekt fit for my problem. I am using it for a small QP with 6 variables and 80 unequality constraints und so far it even outperforms my goto solver qpOASES.

The solver runs on an embbeded hardware and solves an inverse kinematic problem with graduallly changing objective function and constraints. In between steps the the parameter changes are therefore small. Could you comment on how to poperly warstart the solver from the previous solution?

So far I am using update_ldp() followed by daqp_solve() because that is what in you do in the Matlab .update() and .solve() method. But I am not sure if update_ldp() is really neccessary.

By the way your Matlab documentation has a typo. The command d.solve(H,f,A,bupper,blower,sense) does not work.

Best wishes

Julian

are Python 3.12 wheels possible ?

integer variable

how to set x to be integer

if I want to use daqp to solve integer qp, must I transfer integer variable into binary variable?

if I want to use daqp to solve integer qp, must I transfer integer variable into binary variable?

Cvxpy interface help/suggestions

Hello @darnstrom and thanks for publishing DAQP! I started working on an interface to call it from CVXPY, work is here cvxpy/cvxpy#2312 , I wonder if you have any comments or suggestions about it. Happy to give you write privileges on that branch if you'd like to make any change. Thanks!

Add function to add "exact regularization" for MIQPs

See Section 3.1 in BnBDAQP paper

Segmentation Fault on Python Example

Hi Daniel,

I'm trying to run your example for Python and I'm getting segfault on the call to the solver. I followed your installation steps on two different machines running Ubuntu 20.04, and the result was the same. In particular, on my personal machine, I tried to install to a ~/.local prefix, to ensure that there were no issues with permissions accessing the library. This is my result:

➜  ~ ipython3
Python 3.8.10 (default, Jun 22 2022, 20:18:18) 
Type 'copyright', 'credits' or 'license' for more information
IPython 8.4.0 -- An enhanced Interactive Python. Type '?' for help.

In [1]: import daqp
   ...: import numpy as np
   ...: from ctypes import *
   ...: import ctypes.util
   ...: 
   ...: # Define the problem
   ...: H = np.array([[1, 0], [0, 1]],dtype=c_double)
   ...: f = np.array([1, 1],dtype=c_double)
   ...: A = np.array([[1, 1], [1, -1]],dtype=c_double)
   ...: bupper = np.array([1,2,3,4],dtype=c_double)
   ...: blower = np.array([-1,-2,-3,-4],dtype=c_double)
   ...: sense = np.array([0,0,0,0],dtype=c_int)

In [2]: d = daqp.daqp()
   ...: (xstar,fval,exitflag,info) = d.quadprog(H,f,A,bupper,blower,sense)
id cand:  []
double free or corruption (out)
[1]    38052 abort (core dumped)  ipython3

And on pure python3 shell:

➜  ~ python3
Python 3.8.10 (default, Jun 22 2022, 20:18:18) 
[GCC 9.4.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> # Import relevant modules 
>>> import daqp
>>> import numpy as np
>>> from ctypes import * 
>>> import ctypes.util
>>> 
>>> # Define the problem
>>> H = np.array([[1, 0], [0, 1]],dtype=c_double)
>>> f = np.array([1, 1],dtype=c_double)
>>> A = np.array([[1, 1], [1, -1]],dtype=c_double)
>>> bupper = np.array([1,2,3,4],dtype=c_double)
>>> blower = np.array([-1,-2,-3,-4],dtype=c_double)
>>> sense = np.array([0,0,0,0],dtype=c_int)
>>> d = daqp.daqp()
>>> (xstar,fval,exitflag,info) = d.quadprog(H,f,A,bupper,blower,sense)
id cand:  []
free(): invalid next size (fast)
[1]    38371 abort (core dumped)  python3

Can you double check this on your side on a clean Ubuntu install or a CI system? Let me know if I can provide anything to help with this :)

Pedro,

Use DAQP with inequalities constraints and an equality constraint

Your example only features a quadratic program with inequality constraints, the problem I want to solve is :
minimize $0.5 x^THx$
with $\sum_i x_i = 1$ and $\forall i, x_i>0$.

What is the preferred/advised way to implement to solve this problem with your API in Python?

Also the following note in your documentation is not completely clear to me:

Note: When b_lower and b_upper have more elements than the number of rows in A, the first elements of b_lower and b_upper are interpreted as simple bounds.

This means that the additional first elements of b_lower and b_upper are simple bounds for every coordinate of x (eg every $x_i$)?

First attempt (the first row of A gives the sum equals to one constraint):

import numpy as np

import cvxopt
import daqp
import ctypes
import ctypes.util

    # some symmetric matrix
    H = compute_symmetric_matrix(grads)

    n = grads.shape[1]
    f = np.zeros(n,dtype=ctypes.c_double)
    A = np.eye(n+1,dtype=ctypes.c_double)
    # sum = 1 constraint
    A[0, :] = 1.0

    blower = np.zeros(n,dtype=ctypes.c_double)
    bupper = np.ones(n+1,dtype=ctypes.c_double)

    # most are constraints 0<alpha<1
    sense = np.zeros(n,dtype=ctypes.c_double)
    # sum = 1 constraint
    sense[0] = 5

    (xstar,fval,exitflag,info) = daqp.solve(H,f,A,bupper,blower,sense)

Second attempt

    H = compute_symmetric_matrix(grads)

    n = grads.shape[1]
    f = np.zeros(n,dtype=ctypes.c_double)
    # sum = 1 constraint
    A = np.ones((1,n),dtype=ctypes.c_double)
    # x>=0 constraint
    blower = np.zeros(2,dtype=ctypes.c_double)

    # most are constraints 0<alpha<1
    sense = np.zeros(2,dtype=ctypes.c_double)
    # sum = 1 constraint
    sense[1] = 5

    (xstar,fval,exitflag,info) = daqp.solve(H,f,A,bupper,blower,sense)

Best regards.