Convergence bounds for nonlinear programming algorithms

Bounds on convergence are given for a general class of nonlinear programming algorithms. Methods in this class generate at each interation both constraint multipliers and approximate solutions such that, under certain specified assumptions, accumulation points of the multiplier and solution sequences satisfy the Fritz John or the Kuhn—Tucker optimality conditions. Under stronger assumptions, convergence bounds are derived for the sequences of approximate solution, multiplier and objective function values. The theory is applied to an interior—exterior penalty function algorithm modified to allow for inexact subproblem solutions. An entirely new convergence bound in terms of the square root of the penalty controlling parameter is given for this algorithm.