On a second-order step-size algorithm

Abstract

In this paper we present a modification of the second-order step-size algorithm. This modification is based on the so called forcing functions. It is proved that this modified algorithm is well-defined. It is also proved that every point of accumulation of the sequence generated by this algorithm is a second-order point of the nonlinear programming problem. Two different convergence proofs are given having in mind two interpretations of the presented algorithm.