Milanka D. Gardašević-Filipovoć, Nada I. Djuranović-Miličić

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Abstract. In this paper we present a method for minimization of a
nondifferentiable function. The method uses trust region strategy combined with a conjugate subgradient method. It is proved that the
sequence of points generated by the algorithm has an accumulation point
which satisfies the first order necessary and sufficient conditions.


non-smooth convex optimization, trust region method, conjugate subgradient method, bundle methods

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Bonnans J.F., J.C. Gilbert, C. Lemarchal, and C.A. Sagastizbal, Numerical Optimization. Theoretical and Practical Aspects, Springer, (2006)

Browien J., Lewis A., Convex analysis and nonlinear optimization, Canada (1999)

Clarke F. H, Optimization and Nonsmooth Analysis,Wiley, New York,(1983)

Demyanov, V.F., Vasiliev, P.V., Nondifferentiable Optimization. Moscow, Nauka, 384 pp. (in Russian) (1981)

Djuranovic- Milicic N., Gardasevic -Filipovic M., A Multi-step Curve Search Algorithm in Nonlinear Optimization - Nondifferentiable Convex Case, Facta Universitatis Series Mathematics and Informatics, Vol.25, pp 11-24, (2010),

Djuranovic- Milicic N., Gardasevic -Filipovic M.,., An Algorithm For Minimization Of A Nondifferentiable Convex Function, Lecture Notes in Engineering and Computer Science, WCE 2009, VOL. II, pp 1241-1246, (2009)

Djuranovic- Milicic N., Gardasevic -Filipovic M.,., On An Algorithm In Nondifferential Convex Optimization, YUJOR Vol.22 , No. 2 (2012),

Djuranovic- Milicic N., Gardasevic -Filipovic M.,., Nondifferentiable Convex Optimization: An Algorithm Using Moreau-Yosida Regularization, Lecture Notes in Engineering and Computer Science, WCE 2012, VOL. I, pp 131-136, (2012),

Ermoliev, Y. M.; Kryazhimskii, A. V.; Ruszczynskii, A., Constraint Aggregation Principle in Convex Optimization, Mathematical Programming 76 , No. 3, pp 53-372,(1997),

Fletcher R.,Practical Methods of Optimization, Volume 2, Department of Mathematics, University of Dundee, Scotland, U.K, Wiley-Interscience, Publication, (1981),

Fuduli A., Metodi Numerici per la Minimizzazione di Funzioni Convesse Nondifferenziabili, PhD Thesis, Departimento di Electronica Informatica e Sistemistica,Univerzita della Calabria, (1998),

Gardasevic Filipovic M., Djuranovic Milicic N.,An Algorithm Using Trust Region Strategy For Minimization Of A Nondifferentiable Function, Numerical Functional Analysis and Optimization, Vol. 32, No. 12, pp. 1239-1251, (2011),

Gardasevic Filipovic M., Djuranovic Milicic N.,An Algorithm Using Moreau-Yosida Regularization for Minimization of a Nondifferentiable Convex Function, Filomat 27:1, pp 13-20, (2013),

Karas E., Ribeiro A., Sagastizbal C., Solodov M., A bundle-filter method for nonsmooth convex constrained optimization, Mathematical Programming 116, No. 1-2,pp 297-320, (2009),

Kiwiel K., Convergence Of Approximate And Incremental Subgradient Methods For Convex Optimization, SIAM Journal on Optimization, Vol 14, Issue 5, pp 807-840,(2004),

Kiwiel, K., Proximity Control in Bundle Methods for Convex Nondifferentiable Minimization, Mathematical Programming 46, No. 1, pp 105-122, (1990),

Kusarev A.G., Kutateladze S.S., Subdifferential Calculus, Moscow, Nauka, 224 pp (in Russian), 1987,

Lemarechal, C., Nemirovskii, A.; Nesterov, Y, New Variants of Bundle Methods, Mathematical Programming, Vol. 69, No. 1,pp 111-147, (1995),

Lemarechal C., Sagastizabal C., Practical aspects of the Moreau-Yosida regularization I: theoretical preliminaries, SIAM Journal on Optimization, Vol.7, pp 367-385,(1997),

Lemarechal, C.; Strodiot, J.; Bihain, A, On a Bundle Method for Nonsmooth Optimization, In Nonlinear Programming 4; Mangasarian, O. L.; Meyer, R. R.; Robinson,S. M. Eds. pp 245-282.Academic Press: New York, (1981),

Makela M., Survey of Bundle Methods For Nonsmooth Optimization, Optimization Methods and Software, Vol 17, pp. 1-29, (2002),

Meng F., Zhao G., On Second-order Properties of the Moreau-Yosida Regularization for Constrained Nonsmooth Convex Programs, Numer. Funct. Anal. Optim , Vol. 25;No. 5/6, pp 515-530, (2004),

Qi L., Second Order Analysis of the Moreau-Yoshida Regularization, School of Mathematics, The University of New Wales Sydney, New South Wales 2052, Australia,(1998),

Rockafellar R., Convex Analysis, Princeton University Press, New Jersey (1970),

Sagastizabal C., Solodov M., An Infeasible Bundle Method For Nonsmooth Convex Constrained Optimization Without A Penality Function Or A Filter, SIAM Journal of Optimization, Vol. 16, No. 1., pp 146-169, (2005),

Sun W., Yuan Y., Optimization theory and methods, Nonlinear programming, ISBN-10:0-387-24975-3 Springer Science+Business Media, LLC, (2006),

Shor N.Z., Zhurbenko N.G., A minimization method using the operation of extension of the space in the direction of the difference of the two successive gradients, Cybernetics, 7(3), pp 450 - 459, (1971),

Shor N.Z., Minimization Methods for Non-Differentiable Functions, Springer-Verlag,Berlin, Heidelberg, New York, Tokyo, (1985),

Wolfe P., A Method of Conjugate Subgradients for Minimizing Nondifferentiable Functions, Nondifferentiable Optimization, Mathematical Programming Study 3, (Eds.Balinski M. L. and Wolfe P.), pp 145-173, (1975).


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