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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 30459, 11 pages
http://dx.doi.org/10.1155/IJMMS/2006/30459

Duality without constraint qualification in nonsmooth optimization

Department of Mathematics, University of Isfahan, Isfahan 81745-163, Iran

Received 7 May 2005; Revised 26 July 2005; Accepted 1 January 2006

Copyright © 2006 Hindawi Publishing Corporation. 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. M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming. Theory and Algorithms, John Wiley & Sons, New York, 1993. View at Zentralblatt MATH
  2. V. Chankong and Y. Y. Haimes, Multiobjective Decision Making. [Theory and Methodology], vol. 8 of North-Holland Series in System Science and Engineering, North-Holland, New York, 1983. View at Zentralblatt MATH · View at MathSciNet
  3. F. H. Clarke, Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, New York, 1983. View at Zentralblatt MATH · View at MathSciNet
  4. F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski, Nonsmooth Analysis and Control Theory, vol. 178 of Graduate Texts in Mathematics, Springer, New York, 1998. View at Zentralblatt MATH · View at MathSciNet
  5. R. R. Egudo, T. Weir, and B. Mond, “Duality without constraint qualification for multiobjective programming,” Journal of the Australian Mathematical Society. Series B: Applied Mathematics, vol. 33, no. 4, pp. 531–544, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. V. Jeyakumar, “On optimality conditions in nonsmooth inequality constrained minimization,” Numerical Functional Analysis and Optimization, vol. 9, no. 5-6, pp. 535–546, 1987. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. O. L. Mangasarian and S. Fromovitz, “The Fritz John necessary optimality conditions in the presence of equality and inequality constraints,” Journal of Mathematical Analysis and Applications, vol. 17, pp. 37–47, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. T. Weir and B. Mond, “Duality for generalized convex programming without a constraint qualification,” Utilitas Mathematica, vol. 31, pp. 233–242, 1987. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. T. Weir and B. Mond, “Multiple objective programming duality without a constraint qualification,” Utilitas Mathematica, vol. 39, pp. 41–55, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. P. Wolfe, “A duality theorem for non-linear programming,” Quarterly of Applied Mathematics, vol. 19, pp. 239–244, 1961. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet