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Generalized (η,ρ)-Invex Functions and Semiparametric Duality Models for Multiobjective Fractional Programming Problems Containing Arbitrary Norms

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In this paper, we construct several semiparametric duality models and prove appropriate duality theorems under various generalized (η,ρ)-invexity assumptions for a multiobjective fractional programming problem involving arbitrary norms.

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References

  1. Ben-Israel A. and Mond B. (1986). What is invexity?. Journal of the Australian Mathematical Society Series B 28:1–9

    Google Scholar 

  2. Craven B.D. (1981). Invex functions and constrained local minima. Bulletin of the Australian Mathematical Society 24:357–366

    Google Scholar 

  3. Giorgi G. and Guerraggio A. (1996). Various types of nonsmooth invex functions. Journal of Information and Optimization Sciences 17:137–150

    Google Scholar 

  4. Giorgi G. and Mititelu S. (1993). Convexités généralisées et propriétés. Revue Roumaine des Mathématique Pures et Appliquées 38:125–172

    Google Scholar 

  5. Hanson M.A. (1981). On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications 80: 545–550

    Article  Google Scholar 

  6. Hanson M.A. and Mond B. (1982). Further generalizations of convexity in mathematical programming. Journal of Infomation and Optimization Sciences 3:25–32

    Google Scholar 

  7. Horn R.A. and Johnson C.R. (1985). Matrix Analysis. Cambridge University Press, New York

    Google Scholar 

  8. Jeyakumar V. (1985). Strong and weak invexity in mathematical programming. Methods of Operations Research 55: 109–125

    Google Scholar 

  9. Kanniappan P. and Pandian P. (1996). On generalized convex functions in optimization theory – A survey. Opsearch 33:174–185

    Google Scholar 

  10. Martin D.H. (1985). The essence of invexity. Journal of Optimization Theory and Applications 47:65–76

    Article  Google Scholar 

  11. Miettinen K.M. (1999). Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston

    Google Scholar 

  12. Mititelu S. and Stancu-Minasian I.M. (1993). Invexity at a point: Generalizations and classification. Bulletin of the Australian Mathematical Society 48:117–126

    Google Scholar 

  13. Mond B. and Weir T. (1981). Generalized concavity and duality. In: Schaible S. and Ziemba W.T. (eds). Generalized Concavity in Optimization and Economics. Academic Press, New York, pp. 263–279

    Google Scholar 

  14. Pini R. (1991). Invexity and generalized convexity. Optimization 22:513–525

    Article  Google Scholar 

  15. Pini R. and Singh C. (1997). A survey of recent [1985 – 1995] advances in generalized convexity with applications to duality theory and optimality conditions. Optimizatopm 39:311–360

    Article  Google Scholar 

  16. Sawaragi Y., Nakayama H. and Tanino T. (1986). Theory of Multiobjective Optimization. Academic Press, New York

    Google Scholar 

  17. Reiland T.W. (1990). Nonsmooth invexity. Bulletin of the Australian Mathematical 42:437–446

    Article  Google Scholar 

  18. White D.J. (1982). Optimality and Efficiency. Wiley, New York

    Google Scholar 

  19. Yang X. (1994). Generalized convex duality for multiobjective fractional programs. Opsearch 31:155–163

    Google Scholar 

  20. Yu P.L. (1985). Multiple-Criteria Decision Making: Concepts, Techniques, and Extensions. Plenum Press, New York

    Google Scholar 

  21. Zalmai G.J. (1994). Optimality conditions and duality models for a class of nonsmooth constrained fractional variational problems. Optimization 30:15–51

    Article  Google Scholar 

  22. Zalmai G.J. (1996). Continuous-time multiobjective fractional programming. Optimization 37:1–25

    Article  Google Scholar 

  23. Zalmai G.J. (1996). Proper efficiency conditions and duality models for nonsmooth multiobjective fractional programming problems with operator constraints, Part I : Theory. Utilitas Mathematica 50:163–202

    Google Scholar 

  24. Zalmai G.J. (1997). Proper efficiency conditions and duality models for nonsmooth multiobjective fractional programming problems with operator constraints, part II : Applications. Utilitas Mathematica 51:193–237

    Google Scholar 

  25. Zalmai G.J. (1998). Proper efficiency principles and duality models for a class of continuous-time multiobjective fractional programming problems with operator constraints. Journal of Statistics and Management Systems 1:11–59

    Google Scholar 

  26. Zalmai, G.J. (2006). Generalized (η,ρ)-invex functions and global semiparametric sufficient efficiency conditions for multiobjective fractional programming problems containing arbitrary norms, Journal of Global Optimization (forthcoming).

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Zalmai, G.J. Generalized (η,ρ)-Invex Functions and Semiparametric Duality Models for Multiobjective Fractional Programming Problems Containing Arbitrary Norms. J Glob Optim 36, 237–282 (2006). https://doi.org/10.1007/s10898-006-9008-1

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  • DOI: https://doi.org/10.1007/s10898-006-9008-1

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