The affine-scaling algorithm was initially developed for linear programming problems. Its extension to problems with a nonlinear objective performs at each iteration a scaling followed by a line search along the steepest descent direction. In this paper we prove that any accumulation point generated by this algorithm when applied to a convex function is an optimal solution, under a primal non-degeneracy hypothesis and very general line search procedures.
Report ES-238/90, COPPE - Federal University of Rio de Janeiro, 1990. Revised in September 2002.