A comprehensive collection of implementations and comparisons of numerical optimization algorithms, from classical least squares to modern techniques for inverse problems and optimal control in epidemiological modeling.
Each script includes:
- Mathematical formulation,
- Multiple algorithmic approaches,
- Convergence analysis,
- Visual comparison of trajectories and objective values,
- Robustness testing under noise and ill-conditioning.
| Problem | Methods Compared |
|---|---|
| Linear Least Squares | Analytical solution for y = c路x with noise |
| Gradient Descent | Constant step, Armijo backtracking, Nesterov acceleration |
| Ill-Conditioned Systems | SVD analysis, condition number, regularization impact |
| Steepest Descent | With Tikhonov regularization (位-sweep) |
| Nonlinear Optimization | Noisy non-convex function + L2 regularization |
| Inverse Problem (SEIR) | Gradient descent, Simulated Annealing, Nelder-Mead |
| Optimal Control (SEIR) | Forward-backward sweep for vaccination/treatment strategies |