POSITIVE BASIS AND A CLASS OF DIRECT SEARCH TECHNIQUES

A unified convergent theorem is given for a class of direct scarch techniques in nonlinear programming. This class of techniques is defined as the descent method with fixed step size. It tins the following techniques as its special cases: the axis directional search technique, Hooke-Jeeves technique and the simplified and varied Hooke-Jeeves techniques given, in this paper. Thus the convergence of these techniques can be obtained from the above unified convergent theorem. Besides, the same idea may be applied to the analysis of the simplex evolutionary technique which will be given by the author in a separate paper. For these purposes, a study of positive basis in algebra is made in the first part of this paper.