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A global convergence theory for a broad class of ''monotonic'' nonlinear programming algorithms is given. The key difference between the approach presented here and previous work in this area by Zangwill, Meyer, and others lies in the use of an appropriate definition of a fixed point of a point-to-set mapping. The use of this fixed-point concept allows both a simplification and a strengthening and extension of previous results. In particular, actual convergence of the entire sequence of iterates (as opposed to subsequential convergence) and point-of-attraction theorems are established under weak hypotheses. Examples of the application of this theory to feasible direction algorithms are given.