CVXPY-CODEGEN

WARNING: This tool is still in an early stage of development, and many bugs might still exist. Consider it an early alpha, and don't use it for safety-critical applications (yet).

CVXPY-CODEGEN generates embedded C code for solving convex optimization problems. It allows the user to specify a family of convex optimization problems at a high abstraction level using CVXPY in Python, and then solve instances of this problem family in C (possibly on an embedded microcontroller). The generated C code is essentially a wrapper for embedded optimization solvers (currently only ECOS) for the specified family of problems.

Abstractly, CVXPY-CODEGEN addresses parametrized families of convex optimization problems of the form:

minimize    f_0(x, a)
subject to  f_i(x, a) <= 0, for i = 1,...,m.

The parameter a defines a specific problem instance in the family; for every such problem instance, the variable x is to be determined by solving the optimization problem. In CVXPY-CODEGEN, the problem family (ie, the convex functions f_i) are specified in Python using CVXPY. After C code is generated for this family, the user passes in the parameter a, and the problem is solved (all in C). Currently, problems handled include least squares problems, linear programs (LPs), quadratic programs (QPs), second-order cone programs (SOCPs).

Least squares example

To make this all concrete, let's try a simple least-squares problem:

import cvxpy as cvx
from cvxpy_codegen import codegen
m = 10
n = 5
A = cvx.Parameter(m, n, name='A')
b = cvx.Parameter(m, name='b')
x = cvx.Variable(n, name='x')
f0 = cvx.norm(A*x - b)
prob = cvx.Problem(cvx.Minimize(f0))
codegen(prob, 'least_squares_example')

Then the generated code is available in the least_squares_example directory (which is in the currenty directory). The API is contained in the header file codegen.h. To test out the embedded solver on randomly generated data, run

cd ~/least_squares_example
make
./example_problem

If you'd rather not use random data, you can specify the data to be used by adding

import numpy as np
A.value = np.random.randn(m, n)
b.value = np.random.randn(m, 1)

before generating the C code in Python. (Presumably you would replace the random matrices with whatever values you'd like.)

The directory also contains a Python wrapper, so you can use your embedded C solver in Python as a C extension. To install this C extension, navigate over to the directory with the generated code, and type python setup.py install. To use it, import it with import cvxpy_codegen_solver

Optimal control example

As a more sophistocated example, we consider a constrained, linear optimal control problem (such as for model predictive control, or MPC).

import cvxpy as cvx
from cvxpy_codegen import codegen
np.random.seed(0)
n = 5
m = 3
T = 15

A  = cvx.Parameter(n, n, name='A')
B  = cvx.Parameter(n, m, name='B')
x0 = cvx.Parameter(n, 1, name='x0')

x = cvx.Variable(n, T+1, name='x')
u = cvx.Variable(m, T, name='u')

obj = 0
constr = []
constr += [x[:,0] == x0]
for t in range(T):
    constr += [x[:,t+1] == A*x[:,t] + B*u[:,t]]
    constr += [cvx.norm(u[:,t], 'inf') <= 1] 
    obj += cvx.sum_squares(x[:,t+1]) + cvx.sum_squares(u[:,t])

prob = cvx.Problem(cg.Minimize(obj), constr)
codegen(prob, 'opt_ctrl_example')

Installation

To install, clone this repository, cd over the directory of the cloned repo, and run python setup.py install. Currently, CVXPY-CODEGEN is not available through any Python repository. CVXPY-CODEGEN was only tested in Linux with Python 3.5.

Limitations

It is not possible (and will never be possible) to change the dimensions of the parameters within a single family of convex problems.

Sparse parameters are not currently supported.

Due to the way CVXPY currently works, it's not possible to use a parameter as the positive semidefinite matrix in the quad_form atom. (As a partial fix, we can use sum_squares(L*x), using the Cholesky factor L as a parameter instead of the positive semidefinite matrix itself.)

License

CVXPY-CODEGEN is currently licensed under GPL version 3. This is because the only supported backend solver, ECOS, is under GPL version 3. (If you have a different license for ECOS, I'd be more than happy to provide a more permissive license for CVXPY-CODEGEN.) I am planning on adding at least one more solver, in which case the license for the generated code would have the most permissive license compatible with the chosen backend solver.