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Second order mixed symmetric duality in non-diferentiable multi-objective mathematical programming

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Języki publikacji
EN
Abstrakty
EN
A pair of Mond- Weir type second order mixed symmetric duals is presented for a class of non-differen- tiable multi-objective non-linear programming problems with multiple arguments. We establish duality theorems for the new pair of dual models under second order generalized convexity assumptions. This mixed second order dual for- mulation unifies the two existing second order symmetric dual formu- lations in the literature. Many recent works on symmetric duality are obtained as special cases of the results established in the present paper .
Wydawca
Rocznik
Strony
117--132
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
  • Department of Mathematics, Statistics and Computer Science. College of Basic Sciences and Humanities. Govind Ballabh Pant University of Agriculture and Technology. Pantnagar, India, msshas@cityu.edu.hk
Bibliografia
  • [1] Aghezzaf, B., Hachimi, M., Sufficient optimality conditions and duality in multiobjective progmmming involving genemlized convexity, Numer. Funct. Anal. Optim. 22 (2001), 775-788.
  • [2] Antczak, T., Multiobjective programming under d-invexity, European J. Oper. Res. 137 (2002), 28-36.
  • [3] Bector, C. R., Chandra, S., Abha, On mixed symmetric duality in multiobjective programming, Opsearch 36 (1999), 399-407.
  • [4] Chen, X., Higher-order symmetric duality in nondifferentiable multiobjective programming problems, J. Math. Anal. Appl. 290 (2004), 423-435.
  • [5] Dantzig, G. B., Eisenberg, E., Cottle, R. W., Symmetric dual nonlinear programs, Pacific J. Math. 15 (1965), 809-812.
  • [6] Devi, G., Symmetric duality for nonlinear programming problem involving η-convfunctions, European J. Oper. Res. 104 (1998), 615-621.
  • [7] Dorn, W. S., A symmetric dual theorem for quadratic programming, J. Oper. Res. Soc. Japan 2 (1960). 93-97.
  • [8] Hanson, M. A., On sufficiency of the Kuhn-Thcker conditions, J. Math. Anal. Appl. 80 (1981), 545-550.
  • [9] Hanson, M. A., Second order invexity and duality in mathematical programming, Opsearch 30 (1993), 313-320.
  • [10] Hanson, M. A., Mond, B., Further generalization of convexity in mathematical programming, J. Inf. Optim. Sci. 3 (1982), 25-32.
  • [11] Hou, S. H., Yang, X. M., On second order symmetric duality in nondifferentiable programming, J. Math. Anal. Appl. 255 (2001), 491-498.
  • [12] Kaul., R. N., Kaur, S., Optimality criteria in nonlinear progmmming involving nonconvex functions, J. Math. Anal. Appl. 105 (1985), 104-112.
  • [13] Mangasarian, O. L., Second and higher order duality in nonlinear programming, J. Math. Anal. Appl. 51 (1975), 607-620.
  • [14] Mishra, S. K., Multiobjective second order symmetric duality with cone constraints, European J. Oper. Res. 126 (2000),675-682.
  • [15] Mishra, S. K., Second order symmetric duality in mathematical programming with F-convexity, European J. Oper. Res. 127 (2000), 507-518.
  • [16] Mishra, S. K., On second order symmetric duality in mathematical programming, in: "Recent Developments in Operational. Research", M. L. Agarwal and K: Sen (Eds.), Narosa Publishing House, New Delhi, 2001, 261-272.
  • [17] Mishra, S. K., Second order generalized invexity and duality in mathematical programming, Optimization 42 (1997), 51-69.
  • [18] Mond, B., A symmetric dual theorem for nonlinear programs, Quart. Appl. Math. 23 (1965),265-269.
  • [19] Mond, B., Second order duality for nonlinear progmms, Opsearch 11 (1974), 90-99.
  • [20] Mond, B., Schechter, M., Nondifferentiable symmetric duality, Bull. Austral. Math. Soc. 53 (1996), 177-188.
  • [21] Mond, B., Weir, T., Symmetric duality for nonlinear multiobjective progmmming, in: "Recent Developments in Mathematical Programming", S.Kumar(Ed.), Gordon and Breach, London (1991), 137-153. ,
  • [22] Nanda, S., Das, L. N., Pseudo-invexity and duality in nonlinear programming, European J. Oper. Res. 88 (1996), 572-577.
  • [23] Rockafellar, R. T., Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
  • [24] Suneja, S. K., Lalitha, C. S., Khurana, S" Second order symmetric duality in multiobjective programming, European J. Oper. Res. 144 (2003),492-500.
  • [25] Weir, T., Mond, B., Symmetric and self duality in multiobjective progmmming, Asia-Pacific J. Oper. Res. 5 (1988),124-133.
  • [26] Yang, X. M., Yang, x. Q., Teo, K. L., Nondifferentiable second order symmetric duality in mathematical progmmming with F-convexity, European J. Oper. Res. 144 (2003),554-559.
  • [27] Yang, X. M., Teo, K. L" Yang, X. Q., Mixed symmetric duality in nondifferentiable mathematical programming, Indian J. Pure Appl. Math. 34 (2003), 805-815.
  • [28] Yang, X. M., Yang, X. Q., Teo, K. L., Hou, S. H., Second order symmetric duality in non-differentiable multi-objective progmmming with F-convexity, European J. Oper . Res. 164 (2005), 406-416.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD4-0005-0056
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