A Controlled Perturbation Algorithm for Saddle Point Escape of Generic Non-convex Optimization Problems: Algorithm Description – Version 1.0

We introduce the Controlled Perturbation Algorithm (CPA) for escaping saddle points in generic non‑convex optimization problems. The key idea is to use two adaptive perturbations per coordinate, evaluate their directional derivatives, and deterministically select a descent direction – all without computing second or higher order derivatives. We also define the Non‑Descent Direction Approximation (NDDA) index as a cheap heuristic indicator of proximity to a local minimum. This note is a prelimina