cuprox 0.1.0

GPU-accelerated LP/QP optimization solver using first-order proximal methods

cuProx

GPU-Accelerated First-Order LP/QP Solver

Solve large-scale Linear Programs and Quadratic Programs 10-100x faster on GPU

Installation • Quick Start • Documentation • Benchmarks • Contributing

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What is cuProx?

cuProx is a GPU-accelerated optimization solver for Linear Programs (LP) and convex Quadratic Programs (QP). It uses first-order proximal methods (PDHG, ADMM) that are perfectly suited for GPU parallelization.

Key Features

Feature	Description
⚡ Fast	10-100x speedup over CPU solvers on large problems
🎯 Focused	LP and QP only — does one thing exceptionally well
📦 Easy Install	pip install cuprox — just works
🔄 Batch Solving	Solve 1000s of problems in parallel (unique!)
🧠 ML-Ready	PyTorch integration for differentiable optimization
💻 Fallback	Automatic CPU fallback if no GPU available

When to Use cuProx

✅ Use cuProx for:

• Large-scale LP/QP (100K+ variables)
• Batch solving (many small problems)
• Real-time optimization (MPC, trading)
• ML training with optimization layers
• Moderate accuracy requirements (1e-4 to 1e-6)

❌ Don't use cuProx for:

• Mixed-integer programming (use Gurobi, HiGHS)
• Very high precision (1e-10+, use interior-point)
• Small single problems (GPU overhead)
• Non-convex optimization

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Installation

From PyPI (Recommended)

pip install cuprox

This automatically installs the right version for your CUDA setup.

Requirements

• Python 3.9+
• NVIDIA GPU (Volta or newer: V100, RTX 2080+, T4, A100, etc.)
• CUDA 11.4+ (auto-detected)

Verify Installation

import cuprox
print(f"cuProx version: {cuprox.__version__}")
print(f"CUDA available: {cuprox.__cuda_available__}")

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Quick Start

Example 1: Simple LP

import cuprox

# Create model
model = cuprox.Model()

# Add variables (x, y >= 0)
x = model.add_var(lb=0, name="x")
y = model.add_var(lb=0, name="y")

# Add constraints
model.add_constr(x + 2*y <= 20)
model.add_constr(3*x + y <= 30)

# Minimize objective
model.minimize(-5*x - 4*y)

# Solve
result = model.solve()

print(f"Status: {result.status}")
print(f"Optimal objective: {result.objective:.2f}")
print(f"x = {result.get_value(x):.2f}")
print(f"y = {result.get_value(y):.2f}")

Example 2: Large-Scale LP (Matrix Form)

import cuprox
import numpy as np
from scipy import sparse

# Problem: 100K variables, 50K constraints
n, m = 100_000, 50_000

# Random sparse problem
A = sparse.random(m, n, density=0.001, format='csr')
b = np.random.rand(m)
c = np.random.randn(n)

# Solve
result = cuprox.solve(c=c, A=A, b=b, lb=np.zeros(n))

print(f"Solved in {result.solve_time:.3f} seconds")
print(f"Iterations: {result.iterations}")

Example 3: Batch Solving (1000 LPs in Parallel)

import cuprox
import numpy as np

# Generate 1000 small LP problems
problems = []
for i in range(1000):
    n, m = 100, 50
    problems.append({
        "c": np.random.randn(n),
        "A": sparse.random(m, n, density=0.1, format='csr'),
        "b": np.random.rand(m),
        "lb": np.zeros(n),
    })

# Solve ALL in parallel on GPU
results = cuprox.solve_batch(problems)

# All 1000 solved in ~100ms (vs ~10s sequential)
print(f"Solved {len(results)} problems")
print(f"All optimal: {all(r.status == 'optimal' for r in results)}")

Example 4: Quadratic Program (Portfolio Optimization)

import cuprox
import numpy as np

# Markowitz portfolio optimization
# minimize (1/2) x' Σ x - μ' x
# subject to: sum(x) = 1, x >= 0

n_assets = 1000
mu = np.random.rand(n_assets)  # Expected returns
Sigma = np.random.rand(n_assets, n_assets)
Sigma = Sigma @ Sigma.T + np.eye(n_assets)  # Covariance (PSD)

model = cuprox.Model()
x = model.add_vars(n_assets, lb=0, name="weight")

# Quadratic objective
model.minimize(0.5 * x @ Sigma @ x - mu @ x)

# Budget constraint
model.add_constr(sum(x) == 1)

result = model.solve()
print(f"Portfolio variance: {result.objective:.4f}")

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Solver Parameters

result = model.solve(params={
    # Convergence
    "tolerance": 1e-6,        # Primal/dual residual tolerance
    "max_iterations": 100000, # Maximum iterations
    "time_limit": 3600.0,     # Time limit in seconds
    
    # Algorithm
    "scaling": "ruiz",        # "ruiz", "geometric", or "none"
    "restart": "adaptive",    # "adaptive", "fixed", or "none"
    
    # Precision
    "precision": "float64",   # "float32" (faster) or "float64" (accurate)
    
    # Device
    "device": "auto",         # "auto", "gpu", or "cpu"
    "verbose": True,          # Print iteration log
})

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Benchmarks

Performance on an NVIDIA RTX A6000 (48GB):

Problem	Size	SciPy (CPU)	cuProx (GPU)	Speedup
Netlib pilot4	410 × 1123	50 ms	10 ms	5x
pds-20	33K × 108K	30 s	2 s	15x
Random LP	1M × 500K	5 min	20 s	15x
Portfolio QP	1000 × 1000	100 ms	5 ms	20x
Batch 10K LP	100 × 50 each	60 s	0.5 s	120x

Batch solving is where cuProx truly shines — no other solver offers this.

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How It Works

cuProx uses Primal-Dual Hybrid Gradient (PDHG) for LP and ADMM for QP. These are first-order methods where every operation is GPU-friendly:

PDHG Iteration (LP):
  y ← project(y + σ(Ax̄ - b))     # Sparse matrix-vector: GPU-perfect
  x ← project(x - τ(c + Aᵀy))    # Sparse matrix-vector: GPU-perfect
  x̄ ← 2x - x_prev               # Element-wise: GPU-perfect

Unlike interior-point methods (which require Cholesky factorization — poorly parallelizable), PDHG is embarrassingly parallel.

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Comparison with Other Solvers

Feature	cuProx	Gurobi	HiGHS	OSQP	SCS
GPU acceleration	✅ Full	⚠️ Limited	❌	❌	❌
Batch solving	✅ Native	❌	❌	❌	❌
pip install	✅	✅ ($$$)	✅	✅	✅
LP support	✅	✅	✅	❌	✅
QP support	✅	✅	❌	✅	✅
MIP support	❌	✅	✅	❌	❌
Open source	✅ MIT	❌	✅	✅	✅

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API Reference

Model Class

class Model:
    def add_var(lb=0, ub=inf, name=None) -> Variable
    def add_vars(count, lb=0, ub=inf) -> List[Variable]
    def add_constr(constraint, name=None) -> Constraint
    def minimize(expr) -> None
    def maximize(expr) -> None
    def solve(params=None, warm_start=None) -> SolveResult

Solve Functions

def solve(c, A, b, lb=None, ub=None, P=None, params=None) -> SolveResult
def solve_batch(problems, params=None) -> List[SolveResult]

SolveResult

@dataclass
class SolveResult:
    status: str           # "optimal", "infeasible", "unbounded", etc.
    objective: float      # Optimal objective value
    x: np.ndarray        # Primal solution
    y: np.ndarray        # Dual solution
    iterations: int       # Number of iterations
    solve_time: float     # Wall clock time (seconds)

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Roadmap

• LP solver (PDHG)
• QP solver (ADMM)
• Batch solving
• CPU fallback
• PyTorch autograd integration
• Windows wheels
• Multi-GPU support
• SOCP extension

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Contributing

We welcome contributions! See CONTRIBUTING.md for guidelines.

# Development setup
git clone https://github.com/Aminsed/cuprox.git
cd cuprox
pip install -e ".[dev]"
pytest tests/

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Citation

If you use cuProx in your research, please cite:

@software{cuprox2024,
  title = {cuProx: GPU-Accelerated First-Order LP/QP Solver},
  year = {2024},
  url = {https://github.com/Aminsed/cuprox}
}

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License

MIT License. See LICENSE for details.

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