| Abstract | Inspired by the behavior of the blind for hill-climbing using a stick to detect a higher place by drawing a circle, in this talk, we will present a new derivative-free method, i.e., the hill-climbing method with a stick (HiCS), to treat unconstrained optimization. At a given point, the new algorithm can obtain a better state by searching a surface with the length of the stick. This algorithm can capture a neighbourhood of a minimizer of the objective function rather than directly approximating it. A simple but rigorous theory can guarantee the finite-step convergence of the proposed algorithm without convexity assumption. Only one parameter is required to be input in this method which makes it easy for coding. Meanwhile, an economic sampling strategy with the regular simplex of evaluating function values is given to optimize high dimensional problems. Finally, several standard numerical examples have been used to demonstrate its effciency. HiCS shows potential to find the global minimizer by choosing proper searching parameters. |
