Sequential quadratic programming methods as developed by Wilson, Han, and Powell have gained considerable attention in the last few years mainly because of their outstanding numerical performance. Although the theoretical convergence aspects of this method and its various modifications have been investigated in the literature, there still remain some open questions which will be treated in this paper. The convergence theory to be presented, takes into account the additional variable introduced in the quadratic programming subproblem to avoid inconsistency, the one-dimensional minimization procedure, and, in particular, an “ active set” strategy to avoid the recalculation of unnecessary gradients. This paper also contains a detailed mathematical description of a nonlinear programming algorithm which has been implemented by the author. the usage of the code and detailed numerical test results are presented in [5].