optimiz-rs/docs/source/examples.md

Examples

This page lists all available examples and tutorials for OptimizR.

Jupyter Notebooks

All notebooks are located in the examples/ directory.

1. Differential Evolution

File: 01_differential_evolution_tutorial.ipynb

Learn how to use the Differential Evolution optimizer:

• Basic optimization problems (Rosenbrock, Rastrigin, Ackley)
• Strategy comparison (rand/1, best/1, current-to-best/1)
• Parameter tuning (F, CR, population size)
• Convergence analysis and visualization

2. Mean Field Games

File: 02_mean_field_games_tutorial.ipynb

Solve 1D Mean Field Games:

• HJB-Fokker-Planck coupling
• Agent population dynamics
• Nash equilibrium computation
• 3D visualization (time × space × density)

3. Hidden Markov Models

File: 03_hmm_tutorial.ipynb

Train and apply HMMs:

• Baum-Welch training algorithm
• Viterbi decoding
• Gaussian emission models
• Real-world applications (regime detection, speech recognition)

4. MCMC Sampling

File: 04_mcmc_tutorial.ipynb

Bayesian inference with Metropolis-Hastings:

• Sampling from complex distributions
• Adaptive proposal tuning
• Convergence diagnostics
• Posterior analysis

5. Sparse Optimization

File: 05_sparse_optimization_tutorial.ipynb

Sparse methods for high-dimensional data:

• Sparse PCA
• Elastic Net
• ADMM solver
• Feature selection

6. Optimal Control

File: 06_optimal_control_tutorial.ipynb

Solve HJB equations:

• Regime-switching jump diffusions (MRSJD)
• Optimal stopping problems
• Dynamic programming
• Financial applications

7. Risk Metrics

File: 07_risk_metrics_tutorial.ipynb

Time series analysis:

• Hurst exponent estimation
• Half-life calculation
• Mean reversion testing
• Trading signal generation

Python Scripts

Quick examples for copy-paste usage:

Optimize Rosenbrock Function

import numpy as np
from optimizr import DifferentialEvolution

def rosenbrock(x):
    return sum(100.0 * (x[1:] - x[:-1]**2)**2 + (1 - x[:-1])**2)

de = DifferentialEvolution(bounds=[(-5, 5)] * 10)
result = de.optimize(rosenbrock, max_iterations=200)

print(f"Minimum: {result.best_fitness}")

Train HMM on Data

import numpy as np
from optimizr import HMMGaussian

# Load your data
observations = np.load("data.npy")

# Train model
hmm = HMMGaussian(n_states=3)
hmm.fit(observations)

# Predict states
states = hmm.decode(observations)

MCMC Sampling

import numpy as np
from optimizr import MetropolisHastings

def log_posterior(x):
    return -0.5 * np.sum((x - 2)**2)

sampler = MetropolisHastings(log_posterior, initial_state=np.zeros(5))
samples = sampler.sample(n_samples=10000)

Running Examples

To run notebooks:

cd examples/
jupyter notebook

To run Python scripts:

python examples/basic_optimization.py

Contribute Examples

Have a cool use case? Contribute your example:

1. Fork the repository
2. Add your notebook to examples/
3. Ensure it runs without errors
4. Submit a pull request

See Contributing Guide for details.