Moreau Examples

GPU-accelerated differentiable convex optimization — a visual gallery of notebooks showcasing Moreau.

Quick Start

git clone https://github.com/moreau-opt/moreau-examples.git
cd moreau-examples
pip install jupyter numpy scipy matplotlib seaborn torch cvxpy cvxpylayers Pillow
jupyter notebook notebooks/

Moreau install: Follow the install instructions to set up Moreau for your platform before running the notebooks.

Gallery

	Notebook	Description	Features
	Portfolio Optimization	Markowitz mean-variance optimization: CVXPY, moreau.Solver, batched frontier via CompiledSolver, differentiable Jacobians via moreau.torch, warm-started rolling rebalancing.	CompiledSolver moreau.torch batched differentiable warm-start GPU
	MPC Trajectory Control	Model Predictive Control for a 2D vehicle. Closed-loop simulation with warm starting, animated GIF, 16 initial states solved in parallel.	CompiledSolver batched warm-start animation
	Compressed Sensing	1D sparse recovery, 2D image reconstruction via TV minimization, and learning the measurement matrix by differentiating through the reconstruction solver.	CVXPY cvxpylayers differentiable LP
	Schrödinger Bridges	Entropy-regularized optimal transport as a Schrödinger bridge. Batched sweep of 64 mass-conservation penalties via cvxpylayers.	cvxpylayers batched exp-cones animation
	Swarm Motion Planning	100 agents swap positions on a circle without collisions. SCP with batched GPU solves — each round is one CompiledSolver call.	CompiledSolver batched GPU QP SCP
	Predict, then Optimize	Shortest path routing on a 20×20 grid with learned edge costs. End-to-end training through a differentiable LP layer achieves lower regret than two-stage.	cvxpylayers batched differentiable GPU PyTorch animation
	Sudoku	Sudoku via LP relaxation — 729 variables, exact integer solution from convex relaxation. 256 puzzles solved simultaneously.	CompiledSolver batched LP GPU
	Differentiable Contact	Learn friction from observed motion: Coulomb friction cones (SOC3), chain of differentiable contact solves. Shows why smoothed contact (MuJoCo-style) fails where moreau.torch succeeds.	moreau.torch differentiable SOC
	Fair Bandwidth Allocation	Alpha-fairness via power cones: sweep the fairness-throughput tradeoff, then learn optimal link capacities by differentiating through the fair allocation solver.	cvxpylayers differentiable GPU power-cones animation

Feature Matrix

Notebook	Interface	Batched	Differentiable	Warm Start	GPU	Cones
Portfolio	CompiledSolver moreau.torch	✅	✅	✅	✅	zero, nonneg
MPC	CompiledSolver	✅		✅	✅	zero, nonneg
Compressed Sensing	CVXPY cvxpylayers		✅			zero, nonneg
Schrödinger Bridges	cvxpylayers	✅	✅			zero, nonneg, exp
Swarm Planning	CompiledSolver	✅			✅	zero, nonneg
Predict, then Optimize	cvxpylayers	✅	✅		✅	zero, nonneg
Sudoku	CompiledSolver	✅			✅	zero, nonneg
Contact Friction	moreau.torch		✅			SOC
Bandwidth Allocation	cvxpylayers		✅		✅	zero, nonneg, power

Project Structure

moreau-examples/
├── README.md
├── pyproject.toml
├── assets/                    # Pre-rendered thumbnails and GIFs
├── utils/
│   ├── style.py               # Shared color palette + matplotlib theme
│   ├── animation.py           # GIF/animation helpers
│   └── sparse.py              # CSR matrix construction helpers
├── notebooks/
│   ├── portfolio_optimization.ipynb
│   ├── mpc_trajectory.ipynb
│   ├── compressed_sensing.ipynb
│   ├── optimal_transport.ipynb
│   ├── swarm_planning.ipynb
│   ├── predict_then_optimize.ipynb
│   ├── sudoku.ipynb
│   ├── contact_friction.ipynb
│   └── bandwidth_allocation.ipynb
└── scripts/
    └── render_notebooks.py    # Execute all notebooks + extract thumbnails

Requirements

• Python 3.12+
• Moreau
• NumPy, SciPy, Matplotlib, Seaborn, PyTorch, CVXPY, cvxpylayers, Pillow

All notebooks use float64 precision and include committed outputs — you can browse the results on GitHub without running anything.

Links

• Moreau Documentation
• Moreau API Reference

License

Apache 2.0