On a second-order step-size algorithm
DOI:
https://doi.org/10.2298/YJOR0201121DKeywords:
Forcing function, step-size algorithm, second-order conditions.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.References
Amaya, J. (1989) Convergence of curvilinear search algorithms to second order points. Rev. Mat. Apl., 10, 2, 71-79
Đuranović-Miličić, N.I. (1986) An algorithm in constrained optimization. Lecture Notes in Control and Information Sciences, 203-208
Elkin, R. (1968) Convergence theorems for Gauss-Siedel and other minimization algorithms. College Park, Baltimore MD: University of Maryland, doktorska disertacija
McCormick, G.P. (1983) Nonlinear programming: Theory, algorithms and applications. New York, itd: Wiley
Ortega, J.M., Rheinboldt, W.C. (1970) Iterative solution of nonlinear equations in several variables. New York-San Diego, itd: Academic Press
Downloads
Published
Issue
Section
License
Copyright (c) YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.