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Multiobjective programming with new invexities

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Abstract

(Φ, ρ)-invexity and (Φ, ρ)w-invexity generalize known invexity type properties and have been introduced with the intent of extending most of theoretical results in mathematical programming. Here, we push this approach further, to obtain authentic extensions of previously known optimality and duality results in multiobjective programming.

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References

  1. Antczak T., Stasiak A.: (Φ, ρ)-invexity in nonsmooth optimization. Numer. Funct. Anal. Optim. 32, 1–25 (2010)

    Article  MathSciNet  Google Scholar 

  2. Caristi G., Ferrara M., Stefanescu A.: Mathematical programming with (Φ, ρ)-invexity. In: Konov, I.V., Luc, D.T., Rubinov, A.M. (eds.) Generalized Convexity and Related Topics. Lecture Notes in Economics and Mathematical Systems, vol. 583, pp. 167–176. Springer, Berlin (2006)

    Chapter  Google Scholar 

  3. Chinchuluun A., Yuan D.H., Pardalos P.M.: Optimality conditions and duality for nondifferentiable fractional programming with generalized convexity. Ann. Oper. Res. 154, 133–147 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Craven B.D.: Invex functions and constrained local minima. Bull. Aust. Math. Soc. 24, 357–366 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ferrara M., Stefanescu M.V.: Optimality conditions and duality in multiobjective programming with (Φ, ρ)-invexity. Yugoslav J. Oper. Res. 18, 153–165 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hanson M.A.: On sufficiency of Kuhn Tucker conditions. J. Math. Anal. Appl. 30, 545–550 (1981)

    Article  MathSciNet  Google Scholar 

  7. Hanson M.A., Mond B.: Further generalization of convexity in mathematical programming. J. Inf. Optim. Sci. 3, 22–35 (1982)

    MathSciNet  Google Scholar 

  8. Jeyakumar Y.: Strong and weak invexity in mathematical programming. Methods Oper. Res. 55, 109–125 (1985)

    MathSciNet  MATH  Google Scholar 

  9. Liang Z.A, Huang H.X., Pardalos P.M.: Efficiency conditions and duality for a class of multiobjective fractional programming problems. J. Global Optim. 27, 447–471 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lang X.: Optimality conditions and duality for nondifferentiable multiobjective fractional programming problems with (C, α, ρ, d)-convexity. J.Optim. Theory Appl. 148, 197–208 (2011)

    Article  MathSciNet  Google Scholar 

  11. Martin D.H.: The essence of invexity. J. Optim. Theory. Appl. 47, 65–76 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ojha D.B., Mukerjee R.N.: Some results on symmetric duality of multiobjective programmes with generalized (F, ρ) invexity. Eur. J. Oper. Res. 168, 333–339 (2006)

    Article  MATH  Google Scholar 

  13. Preda V.: On efficiency and duality for multiobjective programs. J. Math. Anal. Appl. 166, 365–377 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  14. Vial J.P.: Strong and weak convexity of sets and functions. Math. Oper. Res. 8, 231–259 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  15. Weir T., Mond B.: Generalized convexity and duality in multiple objective programming. Bull. Aust. Math. Soc. 39, 287–299 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  16. Xu Z.: Mixed type duality in multiobjective programming problems. J. Math. Anal. Appl. 198, 621–635 (1995)

    Article  Google Scholar 

  17. Yang X.M., Yang X.Q., Teo K.L.: Non-differentiable second order symmetric duality in mathematical programming with F-convexity. Eur. J. Oper. Res. 144, 554–559 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yuan D.H., Liu X., Chunchuluun A., Pardalos P.M.: Nondifferentiable minimax fractional programming problems with (C, α, ρ, d)-convexity. J.Optim. Theory Appl. 124, 185–199 (2006)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Academy of Economic Studies, Bucharest, Romania

    Maria Viorica Stefanescu

  2. Department SSGES, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy

    Massimiliano Ferrara

  3. Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania

    Anton Stefanescu

Authors
  1. Maria Viorica Stefanescu
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  2. Massimiliano Ferrara
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  3. Anton Stefanescu
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Correspondence to Anton Stefanescu.

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Stefanescu, M.V., Ferrara, M. & Stefanescu, A. Multiobjective programming with new invexities. Optim Lett 7, 855–870 (2013). https://doi.org/10.1007/s11590-012-0466-8

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  • DOI: https://doi.org/10.1007/s11590-012-0466-8

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