optimiz-rs/docs/source/theory/mathematical_foundations.md

Mathematical Foundations

This section provides formulas used across OptimizR algorithms.

Differential Evolution

• Mutation and crossover follow classic DE/rand/1 and best/1 strategies.
• See Storn & Price (1997) for full derivations.

MCMC

• Metropolis-Hastings with Gaussian proposals.
• Acceptance probability: \alpha = \min\left(1, \frac{\pi(x')q(x\mid x')}{\pi(x)q(x'\mid x)}\right).

HMM

• Baum-Welch (EM) for parameter estimation.
• Viterbi for decoding most likely state sequence.