CVXPYgen - Code generation with CVXPY

CVXPYgen takes a convex optimization problem family modeled with CVXPY and generates a custom solver implementation in C. This generated solver is specific to the problem family and accepts different parameter values. In particular, this solver is suitable for deployment on embedded systems. In addition, CVXPYgen creates a Python wrapper for prototyping and desktop (non-embedded) applications.

An overview of CVXPYgen can be found in our manuscript.

CVXPYgen accepts CVXPY problems that are compliant with Disciplined Convex Programming (DCP). DCP is a system for constructing mathematical expressions with known curvature from a given library of base functions. CVXPY uses DCP to ensure that the specified optimization problems are convex. In addition, problems need to be modeled according to Disciplined Parametrized Programming (DPP). Solving a DPP-compliant problem repeatedly for different values of the parameters can be much faster than repeatedly solving a new problem.

For now, CVXPYgen is a separate module, until it will be integrated into CVXPY. As of today, CVXPYgen works with linear, quadratic, and second-order cone programs.

This package has similar functionality as the package cvxpy_codegen, which appears to be unsupported.

Important: When generating code with the ECOS solver, the generated code is licensed under the GNU General Public License v3.0.

Installation

1. Install cvxpygen (on Windows preferably with Python 3.9).

   pip install cvxpygen
   

2. On Linux or Mac, install the GCC compiler. On Windows, install Microsoft Visual Studio with the 'Desktop development with C++' workload. CVXPYgen is tested with Visual Studio 2019 and 2022, older versions might work as well.

3. Optional: If you wish to use the example notebooks located in examples/, install ipykernel, jupyter, matplotlib, and register a new kernel spec with Jupyter.

   pip install ipykernel jupyter matplotlib
   ipython kernel install --user --name=cvxpygen
   

If you wish to use the Clarabel solver, you need to install Rust and Eigen.

Example

We define a simple 'nonnegative least squares' problem, generate code for it, and solve the problem with example parameter values.

1. Generate Code

Let's step through the first part of examples/main.py. Define a convex optimization problem the way you are used to with CVXPY. Everything that is described as cp.Parameter() is assumed to be changing between multiple solves. For constant properties, use cp.Constant().

import cvxpy as cp

m, n = 3, 2
x = cp.Variable(n, name='x')
A = cp.Parameter((m, n), name='A', sparsity=[(0, 0), (0, 1), (1, 1)])
b = cp.Parameter(m, name='b')
problem = cp.Problem(cp.Minimize(cp.sum_squares(A @ x - b)), [x >= 0])

Specify the name attribute for variables and parameters to recognize them after generating code. The attribute sparsity is a list of 2-tuples that indicate the coordinates of nonzero entries of matrix A. Parameter sparsity is only taken into account for matrices.

Assign parameter values and test-solve.

import numpy as np

np.random.seed(0)
A.value = np.zeros((m, n))
A.value[0, 0] = np.random.randn()
A.value[0, 1] = np.random.randn()
A.value[1, 1] = np.random.randn()
b.value = np.random.randn(m)
problem.solve()

Generating C code for this problem is as simple as,

from cvxpygen import cpg

cpg.generate_code(problem, code_dir='nonneg_LS', solver='SCS')

where the generated code is stored inside nonneg_LS and the SCS solver is used. Next to the positional argument problem, all keyword arguments for the generate_code() method are summarized below.

You can find an overview of the code generation result in nonneg_LS/README.html.

2. Solve & Compare

As summarized in the second part of examples/main.py, after assigning parameter values, you can solve the problem both conventionally and via the generated code, which is wrapped inside the custom CVXPY solve method cpg_solve.

import time
import sys

# import extension module and register custom CVXPY solve method
from nonneg_LS.cpg_solver import cpg_solve
problem.register_solve('cpg', cpg_solve)

# solve problem conventionally
t0 = time.time()
val = problem.solve(solver='SCS')
t1 = time.time()
sys.stdout.write('\nCVXPY\nSolve time: %.3f ms\n' % (1000*(t1-t0)))
sys.stdout.write('Primal solution: x = [%.6f, %.6f]\n' % tuple(x.value))
sys.stdout.write('Dual solution: d0 = [%.6f, %.6f]\n' % tuple(problem.constraints[0].dual_value))
sys.stdout.write('Objective function value: %.6f\n' % val)

# solve problem with C code via python wrapper
t0 = time.time()
val = problem.solve(method='cpg', updated_params=['A', 'b'], verbose=False)
t1 = time.time()
sys.stdout.write('\nCVXPYgen\nSolve time: %.3f ms\n' % (1000 * (t1 - t0)))
sys.stdout.write('Primal solution: x = [%.6f, %.6f]\n' % tuple(x.value))
sys.stdout.write('Dual solution: d0 = [%.6f, %.6f]\n' % tuple(problem.constraints[0].dual_value))
sys.stdout.write('Objective function value: %.6f\n' % val)

The argument updated_params specifies which user-defined parameter values are new. If the argument is omitted, all parameter values are assumed to be new. If only a subset of the user-defined parameters have new values, use this argument to speed up the solver.

Most solver settings can be specified as keyword arguments like without code generation. Here, we use verbose=False to suppress printing. The list of changeable settings differs by solver and is documented in <code_dir>/README.html after code generation.

Comparing the standard and codegen methods for this example, both the solutions and objective values are close. Especially for smaller problems like this, the new solve method 'cpg' is significantly faster than solving without code generation.

3. Executable

In the C code, all of your parameters and variables are stored as vectors via Fortran-style flattening (vertical index moves fastest). For example, the (i, j)-th entry of the original matrix with height h will be the i+j*h-th entry of the flattened matrix in C. For sparse parameters, i.e. matrices, the k-th entry of the C array is the k-th nonzero entry encountered when proceeding through the parameter column by column.

Before compiling the example executable, make sure that CMake 3.5 or newer is installed.

On Unix platforms, run the following commands in your terminal to compile and run the program:

cd nonneg_LS/c/build
cmake ..
cmake --build . --target cpg_example
./cpg_example

On Windows, type:

cd nonneg_LS\c\build
cmake ..
cmake --build . --target cpg_example --config release
Release\cpg_example

Tests

To run tests, install pytest via

conda install pytest

and execute:

cd tests
pytest