Python Quick Start

After installing PDHCG, define a model with NumPy or SciPy arrays and call optimize(). See devices for backend selection and execution settings.

Basic QP

Solve \(\min x_1^2 + x_2^2 - 2x_1 - 6x_2\) subject to \(x_1 + x_2 \le 2\) and \(x \ge 0\):

import numpy as np
import scipy.sparse as sp
from pdhcg import Model

model = Model(
    objective_matrix=sp.diags([2.0, 2.0]),
    objective_vector=np.array([-2.0, -6.0]),
    constraint_matrix=sp.csr_matrix([[1.0, 1.0]]),
    constraint_upper_bound=np.array([2.0]),
    variable_lower_bound=np.zeros(2),
)
model.optimize()
print(model.Status, model.ObjVal, model.X)

The optimum is \(x=(0,2)\) with objective \(-8\).

Quick Start with Cone Constraints

Minimize \(z\) with \((v,w,z)\) in a standard second-order cone and \(v=3\), \(w=4\). The optimum is \((3,4,5)\).

import numpy as np
import scipy.sparse as sp
from pdhcg import ConeSpec, ConeType, Model

model = Model(
    objective_vector=np.array([0.0, 0.0, 1.0]),
    constraint_matrix=sp.csr_matrix([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]]),
    constraint_lower_bound=np.array([3.0, 4.0]),
    constraint_upper_bound=np.array([3.0, 4.0]),
    variable_cones=ConeSpec(ConeType.SOC, np.array([0], dtype=np.int32)),
)
model.optimize()
print(model.Status, model.X)

See the model reference for constructor arguments, ConeSpec, warm starts, and results. Solver settings belong in the parameter reference.

CVXPY

With the CVXPY extra installed, import the backend once to register solver="PDHCG":

import cvxpy as cp
import pdhcg.cvxpy_backend  # Registers solver="PDHCG".

x = cp.Variable()
problem = cp.Problem(cp.Minimize(x), [x >= 1])
value = problem.solve(solver="PDHCG", eps=1e-6)
print(problem.status, value, x.value)

The integration supports quadratic objectives and Zero, NonNeg, SOC, PSD, ExpCone, and PowCone3D constraints, with CVXPY's primal and dual conventions. Mixed-integer models are not supported.