"""

Second-Order Cone Program problem generator.

Problem: minimize c'*x

subject to ||A_i*x + b_i|| <= c_i'*x + d_i

"""

import cvxpy as cp

import numpy as np

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

"""

Generate a robust least squares problem (SOCP formulation).

Problem: minimize ||A*x - b||_2 + lambda*||x||_1

Args:

m: Number of measurements

n: Number of variables

seed: Random seed

Returns:

CVXPY Problem with name and size_metrics attributes

"""

if seed is not None:

np.random.seed(seed)

# Generate problem data

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

x_true = np.random.randn(n)

x_true[np.random.rand(n) < 0.8] = 0 # Sparse

b = A @ x_true + 0.1 * np.random.randn(m)

# Formulate as SOCP

x = cp.Variable(n)

t = cp.Variable()

objective = cp.Minimize(t + 0.1 * cp.norm(x, 1))

constraints = [cp.norm(A @ x - b) <= t]

problem = cp.Problem(objective, constraints)

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

problem.name = f"SOCP-RobustLS (m={m}, n={n})"

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

return problem

def generate_portfolio_robust(n_assets=50, seed=None):

"""

Generate a robust portfolio optimization problem (SOCP).

Args:

n_assets: Number of assets

seed: Random seed

Returns:

CVXPY Problem with name and size_metrics attributes

"""

if seed is not None:

np.random.seed(seed)

# Expected returns

mu = np.random.rand(n_assets) * 0.2 + 0.05

# Uncertainty in returns

Sigma_sqrt = np.random.randn(n_assets, n_assets) / np.sqrt(n_assets)

# Risk parameter

gamma = 2.0

# Formulate problem

w = cp.Variable(n_assets)

# Robust objective: minimize worst-case risk - expected return

objective = cp.Minimize(gamma * cp.norm(Sigma_sqrt.T @ w) - mu.T @ w)

constraints = [cp.sum(w) == 1, w >= 0]

problem = cp.Problem(objective, constraints)

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

problem.name = f"SOCP-Portfolio (n={n_assets})"

problem._custom_size_metrics = {"n_assets": n_assets}

return problem

def generate_small(seed=None):

"""Small SOCP (m=100, n=50)."""

return generate_robust_ls(m=100, n=50, seed=seed)

def generate_medium(seed=None):

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

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