Optimization Toolkit

Overview

This repository provides a toolkit for modeling and solving optimization problems, with a focus on energy-based models. It includes:

• A Rust/Node.js library for defining and evaluating quadratic energy functions.
• Theoretical documentation and examples of optimization models from physics, finance, and machine learning.

Repository Structure

• library/: Rust + Neon-based Node.js library for optimization models.
• theory/: Mathematical background and model documentation (model.md).
• simulation/: (Currently empty) Intended for simulation scripts or notebooks.

Key Concepts

The core model minimizes an energy function of the form:

$$ E = \alpha \sum_{ij} A_{ij} b_i b_j + \beta \sum_i C_i b_i $$

This generalizes many problems, including portfolio optimization, spin glasses, neural networks, and image segmentation. See theory/model.md for details and examples.

Library Usage

The library/ folder contains a Rust library with Neon bindings for Node.js. Main features:

• Define a model with parameters (alpha, beta, A, b, C)
• Compute the energy (score) for a given configuration

Build Instructions

Requirements: Node.js and Rust (platform support)

cd library
npm install
npm run build

Example (Node.js)

const { createModel } = require('./index.node');
const alpha = 1.0, beta = 0.5;
const a = [[1, 0], [0, 1]];
const b = [1, -1];
const c = [0.2, 0.3];
const model = createModel(alpha, beta, a, b, c);
console.log(model.score); // Energy value

Available Scripts

• npm install: Installs dependencies and builds the addon
• npm run build: Release build
• npm run debug: Debug build
• npm run cross: Cross-compile for other platforms
• npm test: Run Rust unit tests

Theory

See theory/model.md for:

• Mathematical formulation
• Convex vs. non-convex cases
• Example models: Markowitz, Ising, Hopfield, Graph Cuts, etc.

License

ISC