For solving nonlinear optimization problems, i.e. for the determination of Kuhn-Tucker points a numerical method is proposed. The considerations continue investigations of \textit{M. Best}, \textit{J. Bräuninger}, \textit{K. Ritter} and \textit{S. Robinson} [ibid. 26, 141-153 (1981; Zbl 0458.65053)] and \textit{H. Kleinmichel}, \textit{C. Richter} and the second author [ibid. 29, 289-307 (1982; Zbl 0489.65038)]. In these papers different local methods are combined with a penalty method in such a way that global convergence can be guaranteed. In order to show that the basic principle of coupling is applicable to a number of further globally convergent methods a local Wilson-type method is now initialized by a feasible direction method that uses reduced gradients. In both phases of the method similar subproblems (special quadratic programs) occur. Therefore, in contrast to the papers mentioned above systems of linear equations have to be solved exclusively. Under usual assumptions the algorithm is shown to be globally and superlinearly convergent.