Published 2024-05-02
Keywords
- Continuous functions, Differentiability, Quasi-Newton Method, Trust Region Method, Free Derivative, Optimization Problems,
Abstract
If f is said to be continuous and assumed to be nonlinear on R", the applicability of these
functions has been noticeable over the years; minimizers are points at which f is
nondifferentiable. Particular concern in this paper is the case where gradient and Hessian
matrix cannot easily be computed for any x. This paper presents a free derivative-based
algorithm for the solution of some optimization problems: finite difference representations of
the gradient and Hessian in Quasi Newton method and Derivative Free Trust Region
methods. It was proved that if f has a distinct solution showed that, the step length, (h) ,
generated converges globally. Two test problems were used for practical implementation
with the use of MATLAB software, and the numerical results showed the effectiveness and
robustness of the algorithms, which compared favorably with some existing algorithms.