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http://dx.doi.org/10.14317/jami.2014.153

WOLFE TYPE HIGHER ORDER SYMMETRIC DUALITY UNDER INVEXITY  

Verma, Khushboo (Department of Mathematics, Indian Institute of Technology)
Gulati, T.R. (Department of Mathematics, Indian Institute of Technology)
Publication Information
Journal of applied mathematics & informatics / v.32, no.1_2, 2014 , pp. 153-159 More about this Journal
Abstract
In this paper, we introduce a pair of higher-order symmetric dual models/problems. Weak, strong and converse duality theorems for this pair are established under the assumption of higher-order invexity. Moreover, self duality theorem is also discussed.
Keywords
Higher-order dual models; symmetric duality; Duality theorems; Higher-order invexity;
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1 I. Ahmad, Unified higher-order duality in nondifferentiable multiobjective programming involving cones, Math. Comput. Model. 55 (3-4) (2012), 419-425.   DOI   ScienceOn
2 I. Ahmad, Z. Husain and Sarita Sharma, Higher order duality in nondifferentiable minimax programming with generalized type I functions, J. Optim. Theory Appl. 141 (2009), 1-12.   DOI
3 I. Ahmad and Z. Husain, Nondifferentiable second order symmetric duality in multiobjective programming, Appl. Math. Lett. 18 (2005), 721-728.   DOI   ScienceOn
4 I. Ahmad and Z. Husain, Second order (F, ${\alpha}$, p, d)-convexity and duality in mul- tiobjective programming, Inform. Sci. 176 (2006), 3094-3103.   DOI   ScienceOn
5 M. S. Bazarra and J. J. Goode, On symmetric duality in nonlinear programming, Opera-tions Research, 21 (1) (1973), 1-9.   DOI   ScienceOn
6 X. H. Chen, Higher-order symmetric duality in nonlinear nondifferentiable programs, preprint, Yr. (2002).
7 G. B. Dantzig, E. Eisenberg and R. W. Cottle, Symmetric dual nonlinear programming, Pacific J. Math. 15 (1965), 809-812.   DOI
8 W. S. Dorn, A symmetric dual theorem for quadratic programming, J. Oper. Res. Soc. Japan. 2 (1960), 93-97.
9 T. R. Gulati and G. Mehndiratta, Nondifferentiable multiobjective Mond-Weir type secondorder symmetric duality over cones, Optim. Lett. 4 (2010), 293-309.   DOI
10 S. K. Gupta and N. Kailey, Nondifferentiable multiobjective second-order symmetric duality, Optim. Lett. 5 (2011), 125-139.   DOI   ScienceOn
11 Z. Husain and I. Ahmad, Note on Mond-Weir type nondifferentiable second order symmetric duality, Optim Lett. 2 (2008), 599-604.   DOI
12 D. S. Kim, H. S. Kang, Y. J. Lee and Y. Y. Seo, Higher order duality in multiobjective programming with cone constraints, Optimization. 59 (1) (2010), 29-43.   DOI   ScienceOn
13 O. L. Mangasarian, Nonlinear Programming, McGraw-Hill, New York, Yr. (1969).
14 M. Schechter, More on subgradient duality, J. Math. Anal. Appl. 71 (1979), 251-262.   DOI
15 O. L. Mangasarian, Second and higher-order duality in nonlinear programming, J. Math. Anal. Appl. 51 (1975), 607-620.   DOI   ScienceOn
16 B. Mond, A symmetric dual theorem for nonlinear programming, Q. J. Appl. Math. 23 (1965), 265-269.   DOI
17 B. Mond and J. Zhang, Higher-order invexity and duality in mathematical programming, in: J. P. Crouzeix, et al. (Eds.), Generalized Convexity, Generalized Monotonicity: Recent Results, Kluwer Academic, Dordrecht, pp. 357-372, Yr. (1998).
18 X. M. Yang, K. L. Teo and X. Q. Yang, Higher-order generalized convexity and duality in nondifferentiable multiobjective mathematical programming, J. Math. Anal. Appl. 297 (2004), 48-55.   DOI   ScienceOn
19 X. M. Yang, X. Q. Yang and K. L. Teo, Higher-order symmetric duality in multiobjective mathematical programming with invexity, J. Ind. Manag. Optim. 4 (2008), 335-391.