MOND-WEIR TYPE HIGHER ORDER MINIMAX MIXED INTEGER DUAL PROGRAMMING UNDER GENERALIZED (<i>&#981;, α, ρ</i>)-UNIVEXITY

A. K. Tripathy

doi:10.11948/2013015

2013 Volume 3 Issue 2

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Article navigation > Journal of Applied Analysis & Computation > 2013 > 3(2): 197-211

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A. K. Tripathy. MOND-WEIR TYPE HIGHER ORDER MINIMAX MIXED INTEGER DUAL PROGRAMMING UNDER GENERALIZED (ϕ, α, ρ)-UNIVEXITY[J]. Journal of Applied Analysis & Computation, 2013, 3(2): 197-211. doi: 10.11948/2013015

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A. K. Tripathy. MOND-WEIR TYPE HIGHER ORDER MINIMAX MIXED INTEGER DUAL PROGRAMMING UNDER GENERALIZED (ϕ, α, ρ)-UNIVEXITY[J]. Journal of Applied Analysis & Computation, 2013, 3(2): 197-211. doi: 10.11948/2013015

MOND-WEIR TYPE HIGHER ORDER MINIMAX MIXED INTEGER DUAL PROGRAMMING UNDER GENERALIZED (ϕ, α, ρ)-UNIVEXITY

A. K. Tripathy

Department Mathematics, Trident Academy of Technology, F2/A, Chandaka Industrial Estate, Bhubaneswar, 751024, Odisha, India

Abstract

Abstract

A new generalized class of higher order (ϕ, α, ρ)-univex function is introduced with an example and we formulate Mond-Weir type nondifferentiable higher order minimax mixed integer dual programs and symmetric duality theorems are establishFed.
- Higher order minimax integer dual program /
- higher order(ϕ,α,ρ)-univex function /
- Schwartz inequality /
- additively separable
MSC: 90C29;90C30;49N15

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References

[1]	I. Ahmad, Second order symmetric duality for nondifferentiable minimax mixed integer problem, Southeast Asian Bull. Math., 29(2005), 843-849. Google Scholar
[2]	I. Ahmad and Z. Husain, Nondifferentiable second order symmetric duality, Asia-Pasific J. Oper. Res., 22(2005), 19-31. Google Scholar
[3]	I. Ahmad, Z. Husain and S. Sharma, Higher order duality in nondifferentiable multiobjective programming, Numer. Funct. Anal. Optim., 28(2007), 989-1002. Google Scholar
[4]	I. Ahmad, Z. Husain and S. Sharma, Higher order duality in nondifferentiable minimax programming with generalized type 1 function, J. Optim. Theory Appl., 141(2009), 1-12. Google Scholar
[5]	E. Balas, Minimax and duality for linear and nonlinear mixed integer programming, Integer and Nonlinear Programming, North Holland, Amsterdam, (1970), 385-417. Google Scholar
[6]	A. Batatorescu, Preda and M. Beldiman, Higher order symmetric multiobjective duality involving generalized (F, ρ, γ, b)-convexity, Rev. Roumaine Math. Pure Appl., 52(2007), 619-630. Google Scholar
[7]	C.R. Bector, S. Chandra, S. Gupta and S.K. Suneja, Univex sets, functions and univex nonlinear programming, Lect. Notes in Eco. Math. System, Springer Verlag, Berlin, 405(1994), 1-8. Google Scholar
[8]	X. Chen, Higher order symmetric duality in nondifferentiable multiobjective programming problem, Math. Anal. Appl., 290(2004), 423-435. Google Scholar
[9]	G.B. Dantzing, E. Eisenberg and R.W. Cottle, Symmetric dual Nonlinear programs,, Pacific J. Math., 15(1965), 809-812. Google Scholar
[10]	G. Devi, Symmetric duality for nonlinear programming problem involvingbonvex function, European J. Oper. Res., 104(1998), 615-621. Google Scholar
[11]	W.S. Dorn, A symmetric dual theorem for quadratic programs, J. Oper. Res. Soc. Japan, 2(1960), 93-97. Google Scholar
[12]	T.R. Gulati and S.K. Gupta, Higher order nondifferentiable symmetric duality with generalized F-convexity, J. Math. Anal. Appl., 329(2007), 229-237. Google Scholar
[13]	T.R. Gulati, I. Husain and I. Ahamad, Symmetric duality for nondifferentiable minimax mixed integer programming problems, Optimization, 39(1997), 69-84. Google Scholar
[14]	M.A. Hanson, On sufficiency of the Kuhn -Tucker condition, J. Math. Anal. Appl., 80(1981), 845-850. Google Scholar
[15]	O.L. Mangasarian, Second order and Higher order duality in nonlinear programming, J. Math. Anal. Appl., 51(1975), 607-620. Google Scholar
[16]	S.K. Mishra and N.G. Rueda, Higher order generalized invexity and duality in mathematical programming, J. Math. Anal. Appl., 247(2000), 173-182. Google Scholar
[17]	S.K. Mishra and N.G. Rueda, Higher order generalized invexity and duality in nondifferentiable mathematical programming, J. Math. Anal. Appl., 272(2002), 496-506. Google Scholar
[18]	B. Mond and M. Schecther, Non-differentiable symmetric duality, Bull. Aust. Math. Soc., 53(1996), 177-188. Google Scholar
[19]	B. Mond and J. Zhang, Higher order invexity and duality in mathematical programming, Generalized convexity, Generalized Monotoncity, Recent Results, Edited by J.P.Crouzeix et al, Kluwer Academic Pub., Dordrecht, 1998, 357-372. Google Scholar
[20]	D.B. Ojha, Higher order duality for multiobjective programming involving (ϕ, ρ)-univexity, World Applied Programming, 1(2011), 155-162. Google Scholar
[21]	G.K. Thakur and B.B. Priya, Second order duality for nondifferentiable multiobjective programming involving (ϕ, ρ)-invexity, Kathmandu University J. Sc., Engg. and Tech., 7(2011), 92-104. Google Scholar
[22]	T. Weir and B. Mond, Symmetric and self duality in multiobjective programming, Asia-Pacific J. Oper.Res., 5(1991), 75-87. Google Scholar
[23]	X.M. Yang, K.L. Teo and X.Q. Yand, Higher order generalized convexity and duality in nondifferentiable multiobjective mathematical programming, Edited by J.A.Eberhard, R.Hill, D.Ralph and B.M.Glover, Kluwer Academic Publ. Dordrecht, Appl. Optimization, 30(1999), 101-116. Google Scholar
[24]	J.Zhang, Higher order convexity and duality in multiobjective programming problem, In. Progress in Optimization, Contribution from Australasia,(Eds:A.Eberhard, R.Hill, D.Ralph, B.M.Glover), Kluwer Academic Publisher, Dordrecht-Boston-London, Appl. Optimization, 30(1999), 101-116. Google Scholar