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2011 | 21 | 2 | 317-329

Tytuł artykułu

Random perturbation of the projected variable metric method for nonsmooth nonconvex optimization problems with linear constraints

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
We present a random perturbation of the projected variable metric method for solving linearly constrained nonsmooth (i.e., nondifferentiable) nonconvex optimization problems, and we establish the convergence to a global minimum for a locally Lipschitz continuous objective function which may be nondifferentiable on a countable set of points. Numerical results show the effectiveness of the proposed approach.

Rocznik

Tom

21

Numer

2

Strony

317-329

Opis fizyczny

Daty

wydano
2011
otrzymano
2010-02-09
poprawiono
2010-11-06

Twórcy

  • Department of Mathematics, Faculty of Science, Jazan University, P.B. 2097, Jazan, Saudi Arabia
  • Laboratory of Study and Research in Applied Mathematics, Mohammadia School of Engineers, Mohammed V Agdal University, Ab Ibn sina, BP 765, Agdal, Rabat, Morocco
  • Laboratory of Study and Research in Applied Mathematics, Mohammadia School of Engineers, Mohammed V Agdal University, Ab Ibn sina, BP 765, Agdal, Rabat, Morocco
  • National Institute for Applied Sciences, Rouen, Avenue de l'Université BP 8, Saint-Etienne du Rouvray, France

Bibliografia

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  • Bouleau, N. (1986). Variables Aléatoires et Simulation, Hermann Editions, Paris.
  • Broyden, C. (1970). The convergence of a class of double-rank minimization algorithms, Journal Institute of Mathematics and Its Applications 6(1): 76-90.
  • Correa, R. and Lemaréchal, C. (1993). Convergence of some algorithms for convex minimization, Mathematical Programming 62(2): 261-275.
  • Davidon, W. (1991). Variable metric method for minimization, SIAM Journal on Optimization 1(1): 1-17.
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  • El Mouatasim, A. and Al-Hossain, A. (2009). Reduced gradient method for minimax estimation of a bounded Poisson mean, Journal of Statistics: Advances in Theory and Applications 2(2): 183-197.
  • El Mouatasim, A., Ellaia, R. and Souza de Cursi, J. (2006). Random perturbation of variable metric method for unconstrained nonsmooth nonconvex optimization, International Journal of Applied Mathematics and Computer Science 16(4): 463-474.
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  • Hiriart-Urruty, J.-B. and Lemaréchal, C. (1993). Convex Analysis and Minimization Algorithms II: Advanced Theory and Bundle Methods, Grundlehren der mathematischen Wissenschaften, Vol. 306, Springer-Verlag, Berlin.
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  • Kiwiel, K. (1985). Method of Descent for Nondifferentiable Optimization, Lecture Notes in Mathematics, Vol. 1133, Springer-Verlag, Berlin.
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  • Kryazhimskii, A. (2001). Optimization problems with convex epigraphs. application to optimal control, International Journal of Applied Mathematics and Computer Science 11(4): 773-801.
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  • Luenberger, D. (1973). Introduction to Linear and Nonlinear Programming, Addison-Wesley Publishing Company, London.
  • Luks̃an, L. and Vlc̃ek, J. (2000). Test problems for nonsmooth unconstraint and linearly constraint optimization, Technical Report TR-798, Institute of Computer Sciences, Academy of Sciences of the Czech Republic, Prague.
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Typ dokumentu

Bibliografia

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bwmeta1.element.bwnjournal-article-amcv21i2p317bwm
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