Repository Summary
Checkout URI  https://github.com/asherikov/qpmad.git 
VCS Type  git 
VCS Version  master 
Last Updated  20230103 
Dev Status  MAINTAINED 
CI status  No Continuous Integration 
Released  RELEASED 
Tags  No category tags. 
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Help Wanted (0)
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Packages
Name  Version 

qpmad  1.3.0 
README
qpmad
CI status  Debian package 
Eigenbased, headeronly C++ implementation of GoldfarbIdnani dual active set algorithm for quadratic programming. The package is ROS compatible.
The solver is optimized for performance, for this reason some of the
computations are omitted as described below. See
https://github.com/asherikov/qpmad_benchmark for comparison with qpOASES
and
eiQuadProg
.
Contents
Links
 Doxygen: https://asherikov.github.io/qpmad/
 GitHub: https://github.com/asherikov/qpmad
Features:
Double sided inequality constraints:
lb <= A*x <= ub
. Such constraints can be handled in a more efficient way thanlb <= A*x
commonly used in other implementations of the algorithm.A
can be sparse.Simple bounds:
lb <= x <= ub
.Lazy data initialization, e.g., perform inversion of the Cholesky factor only if some of the constraints are activated.
Works with positivedefinite problems only (add regularization if necessary).
Performs inplace factorization of Hessian and can reuse it on subsequent iterations. Can optionally store inverted Cholesky factor in the Hessian matrix for additional performance gain.
Does not compute value of the objective function.
Does not compute/update Lagrange multipliers for equality constraints.

Three types of memory allocation:
 on demand (default);
 on compile time using template parameters;
 dynamic preallocation using
reserve()
method.
Dependencies:
 C++11 compatible compiler
 cmake >= 3.0
 Eigen >= 3.3.0
 Boost (for C++ tests)
Notes:
Before computing the full step length I check that the dot product of the chosen constraint with the step direction is not zero instead of checking the norm of the step direction. The former approach makes more sense since the said dot product appears later as a divisor and we can avoid computation of a useless norm.
I am aware that activation of simple bounds zeroes out parts of matrix 'J'. Unfortunately, I don't see a way to exploit this on modern hardware  updating the whole 'J' at once is computationally cheaper than doing this line by line selectively or permuting 'J' to collect sparse rows in one place.
Since the solver may arbitrarily choose violated constraints for activation, it always prefers the cheapest ones, i.e., the simple bounds. In particular, this allows to avoid computation of violations of general constraints if there are violated bounds.
Vector 'd' and primal step direction are updated during partial steps instead of being computed from scratch. This, however, does not result in a significant performance improvement.
Documentation and examples
 Precompiled Doxygen documentation: https://asherikov.github.io/qpmad/
 Introductory demo: https://asherikov.github.io/qpmad/DEMO.html [
./test/dependency/demo.cpp
]
FAQ
'Nonnegative step lengths expected' exception
See discussion at https://github.com/asherikov/qpmad/issues/2