User Guide

This guide covers the core concepts and features of CVXPYlayers.

Contents

• Basic Usage
  • Constructor
  • DPP Requirements
  • Calling the Layer
  • Parameter Shapes
  • Using with Neural Networks (PyTorch)
  • Solver Arguments at Call Time
  • Error Handling
• Batched Execution
  • How Batching Works
  • Broadcasting
  • Performance Considerations
  • Batched Gradients
  • JAX: vmap Integration
  • Example: Batch Portfolio Optimization
• Dual Variables
  • Basic Usage
  • Multiple Dual Variables
  • Dual-Only Output
  • Batching
  • Accessing Dual Variables
• Geometric Programs
  • What are Geometric Programs?
  • Basic Usage
  • Solving and Differentiating
  • How It Works
  • DGP Requirements
  • Example: Optimal Sizing
  • Citing
• Solvers
  • Available Solvers
  • Specifying a Solver
  • Solver Arguments
  • SCS Tuning
  • GPU Acceleration with CuClarabel
  • Solver Comparison
  • Troubleshooting

Overview

CVXPYlayers converts CVXPY problems into differentiable layers. The key concepts are:

1. DPP Compliance: Problems must follow Disciplined Parametrized Programming rules

2. Parameters vs Variables: Parameters are inputs; variables are outputs

3. Implicit Differentiation: Gradients computed via the KKT conditions

4. Cone Program Representation: Problems are canonicalized to standard form

Data Flow

Parameters (torch/jax/mlx tensors)
    |
    v
+-------------------+
| Validate & Batch  |  Check shapes, broadcast
+-------------------+
    |
    v
+-------------------+
| Canonicalize      |  CVXPY -> cone program
+-------------------+
    |
    v
+-------------------+
| Solve             |  diffcp/CuClarabel/etc.
+-------------------+
    |
    v
+-------------------+
| Extract Variables |  Map solution back
+-------------------+
    |
    v
Variables (with gradients attached)