On a second-order step-size algorithm

Authors

  • Nada I. Đuranović-Miličić Department of Mathematics, Faculty of Technology and Metallurgy, University of Belgrade, Belgrade

DOI:

https://doi.org/10.2298/YJOR0201121D

Keywords:

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., "Convergence of curvilinear search algorithms to second order points", Revista de Matematcas Aplicadas, 10 (1989) 71-79.

Djuranovic-Miličić, N., "An algorithm in constrained optimization", in: Lecture Notes in Control and Information Sciences, M. Thoma and A. Wyner (eds.), Springer-Verlag, Berlin, 1986, 203-208.

Elkin, R., "Convergence theorems for Gauss-Siedel and other minimization algorithms", Doctoral Thesis, University of Maryland, College Park, 1968.

Mc Cormick, G.P., Nonlinear Programming, Theory, Algorithms and Applications, Wiley, New York, 1983.

Ortega, J., and Rheinboldt, W., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.

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Published

2002-03-01

Issue

Vol. 12 No. 1 (2002)

Section

Research Articles

License

Copyright (c) 2002 YUJOR

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