DNLP — Disciplined Nonlinear Programming

The DNLP package is an extension of CVXPY to general nonlinear programming (NLP). DNLP allows smooth functions to be freely mixed with nonsmooth convex and concave functions, with some rules governing how the nonsmooth functions can be used. For details, see our paper Disciplined Nonlinear Programming.

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Installation

The installation consists of two steps.

Step 1: Install IPOPT via Conda

DNLP requires an NLP solver. The recommended solver is Ipopt, which can be installed together with its Python interface cyipopt:

conda install -c conda-forge cyipopt

Installing cyipopt via pip may lead to issues, so we strongly recommend using the Conda installation above, even if the rest of your environment uses pip.

Step 2: Install DNLP

DNLP is installed by cloning this repository and installing it locally:

git clone https://github.com/cvxgrp/DNLP.git
cd DNLP
pip install .

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Example

Below we give a toy example where we maximize a convex quadratic function subject to a nonlinear equality constraint. Many more examples, including the ones in the paper, can be found at DNLP-examples.

import cvxpy as cp
import numpy as np 
import cvxpy as cp

# problem data
np.random.seed(0)
n = 3
A = np.random.randn(n, n)
A = A.T @ A

# formulate optimization problem
x = cp.Variable(n)
obj = cp.Maximize(cp.quad_form(x, A))
constraints = [cp.sum_squares(x) == 1]

# initialize and solve
x.value = np.ones(n)
prob = cp.Problem(obj, constraints)
prob.solve(nlp=True, verbose=True)
print("Optimal value from DNLP: ", prob.value)

# the optimal value for this toy problem can also be found by computing the maximum eigenvalue of A
eigenvalues  = np.linalg.eigvalsh(A)
print("Maximum eigenvalue:      " , np.max(eigenvalues))

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Supported Solvers

Solver	License	Installation
IPOPT	EPL-2.0	conda install -c conda-forge cyipopt
Knitro	Commercial	pip install knitro (requires license)