A derivative-free random-search algorithm for globally minimizing a nonconvex function that, inspired by a searchlight beam, performs a complete stepping line search along each sampled direction to the boundary before moving to the next — a depth-first strategy contrasting with methods that evaluate a single point per direction. Students learn a geometric convergence framework that models the probability of locating a global optimizer as the relative surface area of a spherical cap on the unit sphere, yielding convergence-in-probability and expected function-evaluation complexity bounds. It achieves higher accuracy than pure random search and improving hit-and-run under equal evaluation budgets, with the advantage growing in higher dimensions.
Proposes depth-first directional search (DFDS), a derivative-free random-search algorithm for global optimization of a continuous nonconvex function over a compact convex set. Where existing directio…