User Guide

This guide covers the core concepts and features of Moreau.

Contents

• Basic Usage
  • Single Problem Solving
  • Accessing Solver Information
  • Solver Status
  • Matrix Requirements
  • Cone Specification
  • Settings
  • Error Handling
• Batched Solving
  • When to Use Batching
  • Three-Step API
  • Value Broadcasting
  • Accessing Batch Results
  • Re-solving with New Data
  • GPU Performance Tips
  • Memory Considerations
• Device Selection
  • Automatic Selection
  • Manual Device Selection
  • Checking Availability
  • Global Default
  • Framework Integration
  • Performance Guidance
• Solver Settings
  • Settings Overview
  • Device Settings
  • Batch Settings
  • Iteration Control
  • Gradient Settings
  • IPM Settings
  • Common Configurations

Overview

Moreau solves convex conic optimization problems:

minimize    (1/2)x'Px + q'x
subject to  Ax + s = b
            s in K

Where K is a Cartesian product of convex cones.

Key Concepts

1. Single vs Batched: Use Solver for one problem, CompiledSolver for many with shared structure

2. Two APIs: NumPy-based core API, plus PyTorch/JAX integrations with autograd

3. Device Selection: Automatic CPU/GPU selection, or manual override

4. Cone Specification: Define constraint types via the Cones class

Data Flow

Problem Data (P, q, A, b, cones)
    |
    v
+-------------------+
| Solver/           |  Validates dimensions, converts to CSR
| CompiledSolver    |
+-------------------+
    |
    v
+-------------------+
| Backend           |  CPU (Rust) or CUDA (C++)
+-------------------+
    |
    v
+-------------------+
| Solution          |  x, z, s arrays + metadata
+-------------------+

Solver vs CompiledSolver

Feature	Solver	CompiledSolver
Use case	Single problem	Batched problems
Input format	Dense or sparse matrices (NumPy/SciPy)	CSR structure
Batching	No	Yes
Setup	Implicit	Explicit setup() call
Best for	Prototyping	Production