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Original Articles

Some superlinearly convergent inexact generalized Newton method for solving nonsmooth equations

Pages 405-417 | Received 23 Jun 2010, Accepted 17 Sep 2010, Published online: 26 Nov 2010

References

  • An , H. B. , Mo , Z. Y. and Liu , X. P. 2007 . A choice of forcing terms in inexact Newton method . J. Comput. Appl. Math. , 200 : 47 – 60 .
  • Birgin , E. G. , Krejić , N. and Martínez , J. M. 2003 . Globally convergent inexact quasi-Newton methods for solving nonlinear systems . Numer. Algorithms , 32 : 249 – 260 .
  • Chen , X. and Qi , L. 1994 . A parametrized Newton method and a quasi-Newton method for nonsmooth equations . Comput. Optim. Appl. , 3 : 157 – 179 .
  • Clarke , F. H. 1990 . Optimization and Nonsmooth Analysis , Philadelphia : SIAM .
  • Dan , H. , Yamashita , N. and Fukushima , M. 2002 . Convergence properties of the inexact Levenberg-Marquardt method under local error bound . Optim. Methods Softw. , 17 : 605 – 626 .
  • Dembo , R. S. , Eisenstat , S. C. and Steihaug , T. 1982 . Inexact Newton methods . SIAM J. Numer. Anal. , 32 : 400 – 408 .
  • Eisenstat , S. C. and Walker , H. F. 1994 . Globally convergent inexact Newton methods . SIAM J. Optim. , 4 : 393 – 422 .
  • Gao , Y. 2001 . Newton methods for solving nonsmooth equations via a new subdifferential . Math. Methods Oper. Res. , 54 : 239 – 257 .
  • Han , S. P. , Pang , J. S. and Rangaraj , N. 1992 . Globally convergent Newton method for nonsmooth equations . Math. Oper. Res. , 17 : 586 – 607 .
  • Kummer , B. 1992 . “ Newton's method based on generalized derivatives for nonsmooth functions: Convergence analysis ” . In Advances in Optimization , Edited by: Oettli , W. and Pallaschke , D. Vol. 382 , 171 – 194 . Berlin : Springer . Lecture Notes in Economics and Mathematical Systems
  • Martínez , J. M. and Qi , L. 1995 . Inexact Newton method for solving nonsmooth equations . J. Comput. Appl. Math. , 60 : 127 – 145 .
  • Mifflin , R. 1977 . Semismooth and semiconvex functions in constrained optimization . SIAM J. Control Optim. , 15 : 959 – 972 .
  • Pang , J. S. and Qi , L. 1993 . Nonsmooth equations: Motivation and algorithms . SIAM J. Optim. , 3 : 443 – 465 .
  • Pu , D. and Tian , W. 2002 . Globally convergent inexact generalized Newton's methods for nonsmooth equations . J. Comput. Appl. Math. , 138 : 37 – 49 .
  • Qi , L. 1993 . Convergence analysis of some algorithms for solving nonsmooth equations . Math. Oper. Res. , 18 : 227 – 244 .
  • L. Qi, C-differential operators, C-differentiability and generalized Newton methods, Applied Mathematics Report, AMR 96/5, University of New South Wales, 1996
  • Qi , L. and Sun , J. 1993 . A nonsmooth version of Newton's method . Math. Program. , 58 : 353 – 367 .
  • Scarf , H. 1973 . The Computation of Economic Equilibria , New Haven : Yale University Press .
  • Śmietański , M. J. 2007 . Inexact quasi-Newton global convergent method for solving constrained nonsmooth equations . Int. J. Comput. Math. , 84 : 1157 – 1170 .
  • Song , Y. , Gowda , M. S. and Ravindran , G. 2000 . On the characterizations of P- and P 0-properties in nonsmooth functions . Math. Oper. Res. , 25 : 400 – 408 .
  • Spedicato , E. 1975 . Computational experience with quasi-Newton algorithms for minimization problems of moderately large size Segrate , , Milano Report CISE-N-175
  • Sun , D. and Han , J. 1997 . Newton and quasi-Newton methods for a class of nonsmooth equations and related problems . SIAM J. Optim. , 7 : 463 – 480 .

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