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Journal of Mathematics
Volume 2013, Article ID 750834, 10 pages
http://dx.doi.org/10.1155/2013/750834
Research Article

A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad 9177948953, Iran

Received 29 August 2012; Accepted 19 November 2012

Academic Editor: Ellina Grigorieva

Copyright © 2013 Hamid Reza Erfanian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. Z. Du, L. Qi, and R. S. Womersley, Recent Advances in Nonsmooth Optimization, World Scientific Publishing, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  2. Y. Zhang, L. Zhang, and Y. Xu, “New filled functions for nonsmooth global optimization,” Applied Mathematical Modelling, vol. 33, no. 7, pp. 3114–3129, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. V. Kamyad, M. H. Noori Skandari, and H. R. Erfanian, “A new definition for generalized first derivative of nonsmooth functions,” Applied Mathematics, vol. 2, no. 10, pp. 1252–1257, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. T. Rockafellar, Convex functions and dual extremum problems [Ph.D. thesis], Harvard University, Cambridge, Mass, USA, 1963.
  5. F. H. Clarke, Necessary conditions for nonsmooth problems in optimal control and the calculus of variations [Ph.D. thesis], University of Washington, Seattle, Wash, USA, 1973. View at MathSciNet
  6. L. Moreau and D. Aeyels, “Optimization of discontinuous functions: a generalized theory of differentiation,” SIAM Journal on Optimization, vol. 11, no. 1, pp. 53–69, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, John Wiley & Sons, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, NY, USA, 1983. View at MathSciNet
  9. X. Chen, “Smoothing methods for nonsmooth, nonconvex minimization, mathematical programming,” Mathematical Programming, vol. 134, no. 1, pp. 71–99, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  10. X. Chen, Z. Nashed, and Q. Liqun, “Convergence of Newton's method for singular smooth and nonsmooth equations using adaptive outer inverses,” SIAM Journal on Optimization, vol. 7, no. 2, pp. 445–462, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. Y. F. Yang, “A new trust region method for nonsmooth equations,” ANZIAM Journal, vol. 44, no. 4, pp. 595–607, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet