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Duality for vector valued B-invex programming

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Generalized Convexity

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 405))

Abstract

In this paper, assuming the functions to be B-invex (B-incave), we discuss duality for a class of multiobjective programming problems concerning properly efficient solutions and relate this to certain vector saddle point of a vector-valued Lagrangian. We also show that the duality for multiobjective fractional programming and some other mathematical programming problems follow as special cases.

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References

  1. C. R. Bector, Mathematical Analysis of Some Nonlinear Programming Problems, Ph.D. Thesis, Department of Mathematics, Indian Institute of Technology, 1968.

    Google Scholar 

  2. C. R. Bector, “Duality in Nonlinear Fractional Programming”, Zeitschrift für Operations Research, 17 (1973), 183–193.

    Article  Google Scholar 

  3. C. R. Bector and S. Chandra, “Duality for Pseudolinear Minmax Programs”, Asia-Pacific Journal of Operational, 3 (1986), 86–94.

    Google Scholar 

  4. C. R. Bector, S. Chandra and C. Singh, “Duality in Multiobjective Fractional Programming”, Proceedings of the International Workshop on “Generalized Concavity Fractional Programming and Economic Applications”, May 30-June 1, 1988. (Eds.) A. Cambini, E. Castagnoli, L. Martein, P. Mazzoleni and S. Schaible, Springer Verlag, 232–241.

    Google Scholar 

  5. C. R. Bector and C. Singh, “B-vex Functions”, Journal of Optimization Theory and Applications, 71 (1991), 237–253.

    Article  Google Scholar 

  6. C. R. Bector, S. K. Suneja and C. S. Lalitha, “ Generalized B-vex Functions and Generalized B-vex Programming”, Journal of Optimization Theory and Applications, 76 (1993), 561–576.

    Article  Google Scholar 

  7. D. Bhatia and R. K. Budhraja, “On a Class of Fractional Functional Programming Problems”, Opsearch, 27 (1990), 225–238.

    Google Scholar 

  8. E. Castagnoli and P. Mazzoleni, “About Derivatives of Some Generalized Concave Functions”, Journal of Information and Optimization Sciences, 10 (1989), 53–64.

    Google Scholar 

  9. S. Chandra, B. D. Craven and B. Mond, “Vector-valued Lagrangian and Multiobjective Fractional Programming Duality”, Numerical Functional Analysis and Optimization, 11 (1990), 239–254.

    Article  Google Scholar 

  10. B. D. Craven, “Lagrangian Conditions and Quasiduality”, Bulletin of Australian Mathematical Society, 16 (1977), 325–339.

    Article  Google Scholar 

  11. R. R. Egudo, “Multiobjective Fractional Duality”, Bulletin of Australian Mathematical Society, 37 (1988), 367–378.

    Article  Google Scholar 

  12. R. N. Kaul and V. Lyall, “A Note on Nonlinear Fractional Vector Maximization” Opsearch, 26 (1989), 108–121.

    Google Scholar 

  13. O. L. Mangasarian, Nonlinear Programming, McGraw - Hill Book Company, U.S.A. (1969).

    Google Scholar 

  14. W. Rodder, “A Generalized Saddle Point Theory, Its Applications to Duality Theory for Linear Vector Optimum Problems”, European Journal of Operational Research, 1 (1977), 55–59.

    Article  Google Scholar 

  15. S. Schaible, “Bibliography in Fractional Programming”, Zeitschrift für Operations Research, 26 (1982), 211–241.

    Article  Google Scholar 

  16. C. Singh, “A Class of Multiple Criteria Fractional Programming Problems”, Journal of Mathematical Analysis and Applications, 115 (1986), 202–213.

    Article  Google Scholar 

  17. S. Suneja and S. Gupta, “Duality in Multiobjective Fractional Programming Problems Involving Nonconvex Functions”, Proceedings of XXIII Annual Convention of Operational Research Society of India (1990), 603–617.

    Google Scholar 

  18. S. K. Suneja, C. Singh and C. R. Bector, “Generalizations of Pre-invex Functions and B-vex Functions”, Journal of Optimization Theory and Applications, 76 (1993), 577–587.

    Article  Google Scholar 

  19. T. Weir and B. Mond, “Generalized Convexity and Duality in Multiple Objective Programming”, Bulletin of Australian Mathematical Society, 39 (1989), 287–299.

    Article  Google Scholar 

  20. T. Weir, “A Dual For Multiobjective Fractional Programming Problem”, Journal of Information and Optimization Sciences, 7 (1986), 261–269.

    Google Scholar 

  21. T. Weir, “A Duality Theorem for a Multiobjective Fractional Optimization Problem”, Bulletin of Australian Mathematical Society, 34 (1986), 415–425.

    Article  Google Scholar 

  22. T. Weir, “On Duality in Multiobjective Fractional Programming”, Opsearch, 26 (1989), 151–158.

    Google Scholar 

  23. T. Weir, “On Strong Pseudoconvexity in Nonlinear Programming Duality”, Opsearch, 27 (1990), 117–121.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Management Sciences, University of Manitoba, Winnipeg, Canada

    C. R. Bector, M. K. Bector, A. Gill & C. Singh

  2. Department of Mechanical and Industrial Engineering, University of Manitoba, Canada

    C. R. Bector, M. K. Bector, A. Gill & C. Singh

  3. Department of Mathematics, St. Lawrence University, Canton, New York, USA

    C. R. Bector, M. K. Bector, A. Gill & C. Singh

Authors
  1. C. R. Bector
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  2. M. K. Bector
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  3. A. Gill
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  4. C. Singh
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Editor information

Editors and Affiliations

  1. Faculty of Economics, Janus Pannonius University, Rákóczi út 80, H-7621, Pécs, Hungary

    Sándor Komlósi

  2. Computer and Automation Institute, Hungary Academy of Sciences, P.O. Box 63, Kende u. 13-17, H-1518, Budapest, Hungary

    Tamás Rapcsák

  3. Graduate School of Management, University of California, 92521, Riverside, CA, USA

    Siegfried Schaible

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© 1994 Springer-Verlag Berlin Heidelberg

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Bector, C.R., Bector, M.K., Gill, A., Singh, C. (1994). Duality for vector valued B-invex programming. In: Komlósi, S., Rapcsák, T., Schaible, S. (eds) Generalized Convexity. Lecture Notes in Economics and Mathematical Systems, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46802-5_27

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  • DOI: https://doi.org/10.1007/978-3-642-46802-5_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57624-2

  • Online ISBN: 978-3-642-46802-5

  • eBook Packages: Springer Book Archive

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