NVXPY

Overview

NVXPY is a Python-based Domain Specific Language (DSL) designed for formulating and solving non-convex programs using a natural, math-inspired API. It is designed to have as similar an interface to CVXPY as possible.

NVXPY is not a solver, it uses solvers from other packages (such as SLSQP, IPOPT, etc.), and includes a built-in Branch-and-Bound solver for mixed-integer nonlinear programs (MINLP).

Features

• Simple, concise, and math-inspired interface
• Codegen compiler for efficient evaluation (85%-99% as fast as native Python)
• Built-in Branch-and-Bound MINLP solver with discrete value constraints
• Graph constructs for clean MIP formulations (wraps networkx)
• Handles gradients seamlessly, even for custom functions

Installation

NVXPY can be installed from PyPi using:

pip install nvxpy

and has the following dependencies:

• Python >= 3.11
• NumPy >= 2.3
• SciPy >= 1.15
• Autograd >= 1.8
• NetworkX >= 3.0
• cyipopt (optional, for IPOPT solver)

Usage

Basic NLP Example

import numpy as np
import nvxpy as nvx

x = nvx.Variable((3,))
x.value = np.array([-5.0, 0.0, 0.0])  # NLPs require a seed

x_d = np.array([5.0, 0.0, 0.0])

obj = nvx.norm(x - x_d)
constraints = [nvx.norm(x) >= 1.0]  # Non-convex!

prob = nvx.Problem(nvx.Minimize(obj), constraints)
prob.solve(solver=nvx.SLSQP)

print(f'optimized value of x: {x.value}')

Mixed-Integer Programming

NVXPY supports integer and binary variables with a built-in Branch-and-Bound solver:

import nvxpy as nvx

# Binary knapsack problem
x = nvx.Variable(integer=True, name="x")
y = nvx.Variable(integer=True, name="y")

prob = nvx.Problem(
    nvx.Maximize(10*x + 6*y),
    [
        5*x + 3*y <= 15,
        x ^ [0, 1],  # x in {0, 1}
        y ^ [0, 1],  # y in {0, 1}
    ]
)
prob.solve(solver=nvx.BNB)

Discrete Value Constraints

Variables can be constrained to discrete sets of values:

x = nvx.Variable(integer=True)

# x must be one of these values
prob = nvx.Problem(
    nvx.Minimize((x - 7)**2),
    [x ^ [1, 5, 10, 15]]  # x in {1, 5, 10, 15}
)
prob.solve(solver=nvx.BNB)  # Optimal: x = 5

Graph-Based MIP Formulations

NVXPY provides Graph and DiGraph constructs for clean graph optimization problems:

import networkx as nx
import nvxpy as nvx

# Maximum Independent Set
nxg = nx.petersen_graph()
G = nvx.Graph(nxg)
y = G.node_vars(binary=True)

prob = nvx.Problem(
    nvx.Maximize(nvx.sum([y[i] for i in G.nodes])),
    G.independent(y)  # y[i] + y[j] <= 1 for all edges
)
prob.solve(solver=nvx.BNB)

Available graph helpers:

• G.edge_vars(binary=True) / G.node_vars(binary=True) - Create decision variables
• G.degree(x) == k - Degree constraints (undirected)
• G.in_degree(x) / G.out_degree(x) - For directed graphs
• G.independent(y) - Independent set constraints
• G.covers(x, y) - Vertex cover constraints
• G.total_weight(x) - Sum of edge weights for objectives

Custom Functions

Wrap arbitrary Python functions using the @nvx.function decorator:

import autograd.numpy as np
import nvxpy as nvx

@nvx.function(jac="autograd")
def rosenbrock(x):
    return (1 - x[0])**2 + 100 * (x[1] - x[0]**2)**2

x = nvx.Variable(shape=(2,))
x.value = np.array([0.0, 0.0])

prob = nvx.Problem(nvx.Minimize(rosenbrock(x)))
prob.solve(solver=nvx.LBFGSB)

Options:

• jac="numerical" - Finite difference gradients (default)
• jac="autograd" - Automatic differentiation via autograd
• jac=callable - User-provided Jacobian function

Available Solvers

Gradient-Free

Solver	Description
nvx.NELDER_MEAD	Derivative-free simplex method
nvx.POWELL	Derivative-free conjugate direction method
nvx.COBYLA	Constrained Optimization BY Linear Approximation
nvx.COBYQA	Constrained Optimization BY Quadratic Approximation

Gradient-Based

Solver	Description
nvx.CG	Conjugate gradient method
nvx.BFGS	Quasi-Newton method
nvx.LBFGSB	Limited-memory BFGS with bounds
nvx.TNC	Truncated Newton method
nvx.SLSQP	Sequential Least Squares Programming (supports constraints)

Hessian-Based

Solver	Description
nvx.NEWTON_CG	Newton-CG trust region method
nvx.DOGLEG	Dogleg trust region method
nvx.TRUST_NCG	Trust-region Newton-CG
nvx.TRUST_KRYLOV	Trust-region with Krylov subspace
nvx.TRUST_EXACT	Trust-region with exact Hessian
nvx.TRUST_CONSTR	Trust-region constrained algorithm

Global Optimizers

Solver	Description
nvx.DIFF_EVOLUTION	Differential evolution
nvx.DUAL_ANNEALING	Dual annealing
nvx.SHGO	Simplicial homology global optimization
nvx.BASINHOPPING	Basin-hopping with local minimization

Other

Solver	Description
nvx.IPOPT	Interior Point Optimizer (requires cyipopt)
nvx.BNB	Built-in Branch-and-Bound MINLP solver

Limitations

NVXPY is in active development. Current limitations:

• Branch-and-Bound solver is basic and may struggle with large problems
• Limited set of atomic operations
• Some edge cases may be untested

Development

To contribute to NVXPY, clone the repository and install the development dependencies:

git clone https://github.com/landonclark97/nvxpy.git
cd nvxpy
poetry install --with dev

Running Tests

Tests are written using pytest. To run the tests, execute:

poetry run pytest

License

Apache 2.0

Contact

For any inquiries or issues, please contact Landon Clark at landonclark97@gmail.com.