We propose a new class of rigorous methods for derivative-free optimization with the aim delivering efficient and robust numerical performance functions all types, from smooth to non-smooth, under different noise regimes. To this end, we have developed methods, called Full-Low Evaluation organized around two main types iterations. The first iteration type (called Full-Eval) is expensive in func...

Derivative-free iterative methods are useful to approximate the numerical solutions when given function lacks explicit derivative information or derivatives too expensive compute. Exploring convergence properties of such is crucial in their development. The behavior approaches and determining practical applicability require conducting local as well semi-local analysis. In this study, we explore...