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2008 | 6 | 3 | 469-481
Tytuł artykułu

A nonsmooth version of the univariate optimization algorithm for locating the nearest extremum (locating extremum in nonsmooth univariate optimization)

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An algorithm for univariate optimization using a linear lower bounding function is extended to a nonsmooth case by using the generalized gradient instead of the derivative. A convergence theorem is proved under the condition of semismoothness. This approach gives a globally superlinear convergence of algorithm, which is a generalized Newton-type method.
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
3
Strony
469-481
Opis fizyczny
Daty
wydano
2008-09-01
online
2008-07-02
Twórcy
Bibliografia
  • [1] Bazaraa M.S., Sherali H.D., Shetty C.M., Nonlinear programming, theory and algorithms, John Wiley & Sons Inc., New York, 1993
  • [2] Bromberg M., Chang T.S., Global optimization using linear lower bounds: one dimensional case, In: Proceedings of the 29th Conference on Decision and Control, Honolulu, Hawaii, 1990
  • [3] Chen X., Superlinear convergence of smoothing quasi-Newton methods for nonsmooth equations, J. Comput. Appl. Math., 1997, 80, 105–126 http://dx.doi.org/10.1016/S0377-0427(97)80133-1
  • [4] Clarke F.H., Optimization and nonsmooth analysis, John Wiley & Sons Inc., New York, 1983
  • [5] Conn A.R., Gould N.I.M., Toint P.L., Trust-region methods, SIAM, Philadelphia, 2000
  • [6] Dennis Jr. J.E., Moré J.J., A characterization of superlinear convergence and its application to quasi-Newton methods, Math. Comp., 1974, 28, 549–560 http://dx.doi.org/10.2307/2005926
  • [7] Famularo D., Sergeyev Ya.D., Pugliese P., Test problems for Lipschitz univariate global optimization with multiextremal constraints, In: Dzemyda G., Saltenis V., Žilinskas A. (Eds.), Stochastic and global optimization, Kluwer Academic Publishers, Dordrecht, 2002
  • [8] Hansen P., Jaumard B., Lu S.H., Global optimization of univariate Lipschitz functions I: survey and properties, Math. Program., 1992, 55, 251–273 http://dx.doi.org/10.1007/BF01581202
  • [9] Harker P.T., Xiao B., Newton’s method for the nonlinear complementarity problem: a B-differentiable equation approach, Math. Program., 1990, 48, 339–357 http://dx.doi.org/10.1007/BF01582262
  • [10] Kahya E., A class of exponential quadratically convergent iterative formulae for unconstrained optimization., Appl. Math. Comput., 2007, 186, 1010–1017 http://dx.doi.org/10.1016/j.amc.2006.08.040
  • [11] Mifflin R., Semismooth and semiconvex functions in constrained optimization, SIAM J. Control Optim., 1977, 15, 959–972 http://dx.doi.org/10.1137/0315061
  • [12] Pang J.S., Newton’s method for B-differentiable equations, Math. Oper. Res., 1990, 15, 311–341 http://dx.doi.org/10.1287/moor.15.2.311
  • [13] Potra F.A., Qi L., Sun D., Secant methods for semismooth equations, Numer. Math., 1998, 80, 305–324 http://dx.doi.org/10.1007/s002110050369
  • [14] Qi L., Sun J., A nonsmooth version of Newton’s method, Math. Program., 1993, 58, 353–367 http://dx.doi.org/10.1007/BF01581275
  • [15] Sergeyev Ya.D., Daponte P., Grimaldi D., Molinaro A., Two methods for solving optimization problems arising in electronic measurements and electrical engineering, SIAM J. Optim., 1999, 10, 1–21 http://dx.doi.org/10.1137/S1052623496312393
  • [16] Shapiro A., On concepts of directional differentiability, J. Optim. Theory Appl., 1990, 66, 477–487 http://dx.doi.org/10.1007/BF00940933
  • [17] Smietanski M.J., A new versions of approximate Newton method for solving nonsmooth equations, Ph.D. thesis, University of Lódz, Poland, 1999 (in Polish)
  • [18] Tseng C.L., A Newton-type univariate optimization algorithm for locating the nearest extremum, Eur. J. Oper. Res., 1998, 105, 236–246 http://dx.doi.org/10.1016/S0377-2217(97)00026-X
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0039-3
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