Modified Sequential Covering Algorithm for Finding a Global Minimizer of Nondifferentiable Functions and Applications

In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We first extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions, and we propose a modification MSCA of this algorithm. We show that the implementation of the algorithm MSCA has the advantage of avoiding the use of auxiliary calculations. The algorithm MSCA is then some what easily which permits to considerably reduce the calculation time. The convergence of the method is also studied. The algorithm MSCA can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.