On the Monotone Convergence of Algorithmic Models zyxwvutsrqponm Ioannis K. Argyros zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH Department of M athematics Cameron University Lawton, Oklahoma 73505-6377 and Ferenc Szidarovszky Sy stems and Industrial Engineering Department University of Arizona Tucson, Arizona 85721 ABSTRACT In this paper we provide first monotone convergence conditions for general algorithmic models. Practical conditions for linear spaces are then derived from the general theory. In particular our results can apply to show monotone conver- gence of Newton-like methods. 1. INTRODUCTION In the theory of nonlinear programming and solution of nonlinear equations, the study of general algorithmic models has included a substan- tial effort to identify properties that will guarantee their convergence in some sense. A comparative study of several convergence conditions was given by Tishyadhigama et al. [9] and their application in optimization problems is given for example in [3]. Their results have been recently extended by Argyros and Szidarovszky [l], and Higle and Sen [2]. In this paper we provide monotone convergence results for nonstation- ary algorithmic models generated by point-to-set maps under very general assumptions. Our results have important applications in developing mono- tonically convergent iterative algorithms in dynamic systems, in input- output analysis, in the solution of nonlinear and differential equations and in optimization problems. (See e.g., [S], [4], [9]). In particular, our results APPLlEDMATHEMATZCSANDCOMPUTATZON48:167-176 zyxwvutsrqponmlkjihgfedcbaZYXW (1992) 167 0 Elsevier Science Publishing Co., Inc., 1992 655 Avenue of the Americas, New York, NY 10010 0096-3003/92/$05.00