"""

Quadratic Program problem generator.

Problem: minimize 0.5*x'*Q*x + c'*x

subject to A*x <= b

"""

import cvxpy as cp

import numpy as np

def generate(n=100, m=50, seed=None):

"""

Generate a quadratic program.

Args:

n: Number of variables

m: Number of inequality constraints

seed: Random seed

Returns:

CVXPY Problem with name and size_metrics attributes

"""

if seed is not None:

np.random.seed(seed)

# Generate positive definite Q

A_mat = np.random.randn(n, n)

Q = A_mat.T @ A_mat / n + 0.1 * np.eye(n)

# Generate linear term

c = np.random.randn(n)

# Generate inequality constraints

A = np.random.randn(m, n)

# Generate feasible point

x_feas = np.random.randn(n)

b = A @ x_feas + np.random.rand(m) + 0.1 # Ensure Ax < b

# Formulate problem

x = cp.Variable(n)

objective = cp.Minimize(0.5 * cp.quad_form(x, Q) + c.T @ x)

constraints = [A @ x <= b]

problem = cp.Problem(objective, constraints)

# Add metadata (use custom attribute since size_metrics is read-only in newer CVXPY)

problem.name = f"QP (n={n}, m={m})"

problem._custom_size_metrics = {"n": n, "m": m}

return problem

def generate_small(seed=None):

"""Small QP (n=50, m=25)."""

return generate(n=50, m=25, seed=seed)

def generate_medium(seed=None):

"""Medium QP (n=500, m=250)."""

return generate(n=500, m=250, seed=seed)

def generate_large(seed=None):

"""Large QP (n=2000, m=1000)."""

return generate(n=2000, m=1000, seed=seed)