Open Access

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

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
Efficient Resource Management for Grid-Enabled Applications (special section, pp. 219 - 306), Joanna Kołodziej and Fatos Xhafa (Eds.)

Bagirov, A. and Yearwood, J. (2006). A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems, European Journal of Operational Research170(2): 578-596.10.1016/j.ejor.2004.06.014Search in Google Scholar

Bogani, C., Gasparo, M.G. and Papini, A. (2009). Generalized pattern search methods for a class of nonsmooth optimization problems with structure, Journal of Computational and Applied Mathematics229(1): 283-293.10.1016/j.cam.2008.10.047Search in Google Scholar

Bouleau, N. (1986). Variables Aléatoires et Simulation, Hermann Editions, Paris.Search in Google Scholar

Broyden, C. (1970). The convergence of a class of double-rank minimization algorithms, Journal Institute of Mathematics and Its Applications6(1): 76-90.10.1093/imamat/6.1.76Search in Google Scholar

Correa, R. and Lemaréchal, C. (1993). Convergence of some algorithms for convex minimization, Mathematical Programming62(2): 261-275.10.1007/BF01585170Search in Google Scholar

Davidon, W. (1991). Variable metric method for minimization, SIAM Journal on Optimization1(1): 1-17.10.1137/0801001Search in Google Scholar

Dorea, C. (1990). Stopping rules for a random optimization method, SIAM Journal on Control and Optimization28(4): 841-850.10.1137/0328048Search in Google Scholar

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 Applications2(2): 183-197.Search in Google Scholar

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 Science16(4): 463-474.Search in Google Scholar

Fletcher, R. (1970). A new approach to variable metric algorithms, Computer Journal13(3): 317-322.10.1093/comjnl/13.3.317Search in Google Scholar

Fletcher, R. and Powell, M. (1963). A rapidly convergent descent method for minimization, Computer Journal6(2): 163-168.10.1093/comjnl/6.2.163Search in Google Scholar

Goldfarb, D. (1970). A family of variable metric methods derived by variational means, Mathematics of Computation24(109): 23-26.10.1090/S0025-5718-1970-0258249-6Search in Google Scholar

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.Search in Google Scholar

Kelley, J. (1960). The cutting plane method for solving convex programs, Journal of the Society for Industrial and Applied Mathematics8(4): 703-712.10.1137/0108053Search in Google Scholar

Kiwiel, K. (1985). Method of Descent for Nondifferentiable Optimization, Lecture Notes in Mathematics, Vol. 1133, Springer-Verlag, Berlin.Search in Google Scholar

Kowalczuk, Z., and Oliski K.O. (2006). Suboptimal fault tolerant control design with the use of discrete optimization, International Journal of Applied Mathematics and Computer Science18(4), DOI: 10.2478/v10006-008-0049-0.10.2478/v10006-008-0049-0Search in Google Scholar

Kryazhimskii, A. (2001). Optimization problems with convex epigraphs. application to optimal control, International Journal of Applied Mathematics and Computer Science11(4): 773-801.Search in Google Scholar

Larsson, T., Patrksson, M. and Stromberg, A. (1996). Conditional subgradient optimization-theory and applications, European Journal of Operational Research88(2): 382-403.10.1016/0377-2217(94)00200-2Search in Google Scholar

Lemaréchal, C., Strodiot, J. and Bihain, A. (1981). On a bundle algorithm for nonsmooth optimization, in O. Mangasarian, R. Meyer and S. Robinson (Eds.), Nonlinear Programming, Vol. 4, Academic Press, New York, NY/London, pp. 245-282.10.1016/B978-0-12-468662-5.50015-XSearch in Google Scholar

Luenberger, D. (1973). Introduction to Linear and Nonlinear Programming, Addison-Wesley Publishing Company, London.Search in Google Scholar

Luksan, L. and Vlcek, 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.Search in Google Scholar

Makela, M. and Neittaanmaki, P. (1992). Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control, World Scientific Publishing Co., London.Search in Google Scholar

Malanowski, K. (2004). Convergence of the Lagrange-Newton method for optimal control problems, International Journal of Applied Mathematics and Computer Science14(4): 531-540.Search in Google Scholar

Panier, E. (1987). An active set method for solving linearly constrained nonsmooth optimization problems, Mathematical Programming37(3): 269-292.10.1007/BF02591738Search in Google Scholar

Peng, Y. and Heying, Q. (2009). A filter-variable-metric method for nonsmooth convex constrained optimization, Applied Mathematics and Computation208(1): 119-128.10.1016/j.amc.2008.11.019Search in Google Scholar

Petersen, I. (2006). Minimax LQG control, International Journal of Applied Mathematics and Computer Science16(3): 309-323.Search in Google Scholar

Pinter, J. (1996). Global Optimization in Action, Kluwer, Dordrecht.10.1007/978-1-4757-2502-5Search in Google Scholar

Pogu, M. and Souza de Cursi, J. (1994). Global optimization by random perturbation of the gradient method with a fixed parameter, Journal of Global Optimization5(2): 159-180.10.1007/BF01100691Search in Google Scholar

Schramm, H. and Zowe, J. (1992). A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results, SIAM Journal of Optimization2: 121-152.10.1137/0802008Search in Google Scholar

Shanno, D. (1970). Conditioning of quasi-Newton methods for function minimization, Mathematics of Computation24(111): 647-657.10.1090/S0025-5718-1970-0274029-XSearch in Google Scholar

Souza de Cursi, J. (1991). Introduction aux probabilités, Ecole Centrale Nantes, Nantes.Search in Google Scholar

Souza de Cursi, J., Ellaia, R. and Bouhadi, M. (2003). Global optimization under nonlinear restrictions by using stochastic perturbations of the projected gradient, in C.A. Floudas and P.M. Pardalos (eds.), Frontiers in Global Optimization, Vol. 1, Dordrecht, Springer, pp.: 541-562.Search in Google Scholar

Uryasev, S. (1991). New variable metric algorithms for nondifferentiable optimization problems, Journal of Optimization Theory and Applications71(2): 359-388.10.1007/BF00939925Search in Google Scholar

Zhang, G. (2009). A note on: A continuous approach to nonlinear integer programming, Applied Mathematics and Computation215(6): 2388-2389.10.1016/j.amc.2009.08.015Search in Google Scholar

ISSN:
1641-876X
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics