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Nondierentiable multiobjective higher-order duality relations for unified type dual models under type-I functions

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초록

The motivation behind this paper is to study a class of nondi erentiable multiobjective fractional program- ming problem in which each component of objective functions contains a term including the support function of a compact convex set. For a di erentiable function, we consider the class of second-order (F; ; ; d)-type- I convex functions. Further, we formulate uni ed (mixed type) dual models and derived duality relations under aforesaid assumptions.

Abstract

The motivation behind this paper is to study a class of nondi erentiable multiobjective fractional program- ming problem in which each component of objective functions contains a term including the support function of a compact convex set. For a di erentiable function, we consider the class of second-order (F; ; ; d)-type- I convex functions. Further, we formulate uni ed (mixed type) dual models and derived duality relations under aforesaid assumptions.

참고문헌 (10)

  1. Ahmad, I., "Unified higher order duality in nondifferentiable multiobjective programming involving cones", Math. Comput. Model, 55, pp.419425~ (2012)
  2. Ramu Dubey, "Optimality and duality results for a nondifferentiable multiobjective fractional programming problem", Journal of Inequalities and Applications, 2015(1) (2015), Springer Science and Business Media LLC[DOI]
  3. Gulati, T.R., "Second-order duality in multiobjective programming involving (F, α p, d)―V -type I functions", Numer. Funct. Anal. Optim, 28, pp.12631277~ (2007)
  4. Gulati, T.R., "Geeta: Duality in nondifferentiable multiobjective fractional programming problem with generalized invexity", J. Appl. Math. Comput, 35, pp.103~118 (2011)
  5. Jayswal, A., "Second order duality for nondifferentiable multiobjective programming problem involving (F, α p, d)―V -type I functions", Optim. Lett, 4, pp.211226~ (2010)
  6. Jayswal, A., "Higher-order duality for multiobjective programming problems involving (F, α p, d)―V -type I functions", J. Math. Model Algor, 13, pp.125141~ (2014)
  7. Mangasarian, O.L., "Second and higher-order duality in nonlinear programming", J. Math. Anal. Appl, 51, pp.607620~ (1975)
  8. Suneja, S.K., "Higher order duality in multiobjective fractional programming with support functions", J. Math. Anal. Appl, 347, pp.817~ (2008)
  9. Yang, "Higher-order generalized convexity and duality in nondifferentiable multiobjective mathematical programming", J.Math. Anal. Appl, 297, pp.4855~ (2004)
  10. Zhang, J., "Progress in Optimization, Contributions from Australasia, Applied Optimization, 30" (1999), Kluwer Academic Publishers

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