A trust region method using subgradient for minimizing a nondifferentiable function

Authors

  • Milanka Gardašević-Filipović Faculty of Architecture, Belgrade

DOI:

https://doi.org/10.2298/YJOR0902249G

Keywords:

Trust region method, non-smooth convex optimization

Abstract

The minimization of a particular nondifferentiable function is considered. The first and second order necessary conditions are given. A trust region method for minimization of this form of the objective function is presented. The algorithm uses the subgradient instead of the gradient. It is proved that the sequence of points generated by the algorithm has an accumulation point which satisfies the first and second order necessary conditions.

References

Алексеев, В.М., Тихомиров, В.М., Фомин, С.В., Оптимальное управление, Наука, Москва, 1979.

Browien, J., and Lewis, A., Convex Analysis and Nonlinear Optimization, Canada, 1999.

Gertz, E.M., and Gill, P.E., “A primal-dual trust-region algorithm for nonlinear optimization”, Math. Program, Ser B, 100 (2004) 49-94.

Fletcher, R., Practical Methods of Optimization, Vol. 1, J. Wiley, New York, 1980.

Fletcher, R., Practical Methods of Optimization, Vol. 2, J. Wiley, New York, 1981.

Fuduli, A., “Metodi numerici per la minimizzazione di funzioni convesse nondifferenziabili”, PhD Thesis, Departimento di Electronica Informatica e Sistemistica, Univerzita della Calabria, 1998.

Кусарев, А.Г., Кутателадзе, С.С., Субдифференциальное исчисление, Издательство Наука, Новосибирск, 1987.

Пшеничный, Б. Н., Метод линеаризации, Наука, Москва, 1983.

Downloads

Published

2009-09-01

Issue

Vol. 19 No. 2 (2009)

Section

Research Articles

License

Copyright (c) 2009 YUJOR

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.