On Holder global optimization method using piecewise affine bounding functions

This paper is devoted to solving the one-dimensional global optimization problems where the objective function f satisfies a Holder condition over a real interval [a , b]. We suggest two algorithms as an extended version of the Piyavskii's method. The first one is based on the use of the tangent at the midpoint of each subinterval of [a , b] of the parabolic lower bounding functions of f . The second one is a combination of two successive phases. In phase 1, we obtain with a few iterations, a subinterval which often contains the point of the global minimum using a K-a-Lipschitz lower bounding functions with a tolerance d much larger than the given accuracy e. In phase 2, we apply the first algorithm on the interval obtained in phase 1. A convergence result is proved and compared with the existing methods. The numerical experiments of the two algorithms on some test functions are encouraging.