Mond-Weir type second order multiobjective mixed symmetric duality with square root term under generalized univex function
DOI:
https://doi.org/10.11121/ijocta.01.2014.00175Keywords:
second order (Φ, Ï)-univex, mixed symmetric duality, efficient solution, square root term, Schwartz inequality.Abstract
In this paper, a new class of second order (Φ,ρ)-univex and second order (Φ,ρ)-pseudo univex function are introduced with example. A pair Mond-Weir type second order mixed symmetric duality for multiobjective nondifferentiable programming is formulated and the duality results are established under the mild assumption of second order (∅,ρ) univexity and second order pseudo univexity. Special cases are discussed to show that this study extends some of the known results in related domain..
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Agarwal, R.P., Ahmad, I., Gupta, S. K. and Kailey, N., Generalized second order mixed symmetric duality in non differentiable mathematical programming, Abstract and Applied Analysis, Hindawi Publishing Corporation, Article ID. 103587, doi: 10.1155/2011/103597 (2011). CrossRef
Aghezzaf, B., Second order mixed type duality in multiobjective programming problems, Journal of Mathematical Analysis and Applications, 285, 97-106 (2003). CrossRef
Ahmad, I. and Husain, Z., Multiobjective mixed symmetric duality involving cones, Computers & Mathematics with Applications, 59 (1), 319-326 (2010). CrossRef
Ahmad, I. and Husain, Z., Nondifferentiable second order duality in multiobjective programming, Applied Mathematics Letters, 18, 721-728 (2005). CrossRef
Ahmad, I. and Sharma, S., Second order duality for non differentiable multiobjective programming, Numerical Functional Analysis and Optimization, 28 (9), 975-988 (2007). CrossRef
Bector, C. R. and Chandra, S., Second order symmetric and self dual programs, Opsearch, 23, 89-95 (1986).
Bector, C. R., Chandra, S. and Abha, On mixed symmetric duality in Mathematical programming, Journal of Mathematical Analysis and Applications, 259, 346-356 (2001). CrossRef
Bector, C. R., Chandra, S. and Goyal, A., On mixed symmetric duality in multiobjective programming, Opsearch, 36, 399-407 (1999).
Chandra, S., Husain, I. and Abha, On mixed symmetric duality in mathematical programming, Opsearch, 36 (2), 165-171 (1999).
Kailey, N., Gupta, S. and Danger, D., Mixed second order multiobjective symmetric duality with cone constraints, Nonlinear Analysis: Real World Applications, 12, 3373-3383 (2011). CrossRef
Li, J. and Gao, Y., Nondifferentiable multiobjective mixed symmetric duality under generalized convexity, Journal of Inequalities and Applications, doi: 10.1186/1029-24x-2011-23 (2011).
Mangasarian, O.L., ‘Second order and higher order duality in nonlinear programming, Journal of Mathematical Analysis and Applications, 51, 607-620 (1975). CrossRef
Mishra, S.K., Second order mixed symmetric duality in nondifferentiable multiobjective mathematical program-ming, Journal of Applied Analysis, 13 (1), 117-132 (2007). CrossRef
Mishra, S. K., Wang, S. Y. and Lai, K. K., Mond-Weir type mixed symmetric first and second order duality in nondifferentiable mathematical program-ming, Journal of Nonlinear and Convex Analysis, 7 (3), 189-198 (2006).
Mishra, S. K., Wang, S. Y., Lai, K. K. and Yang, F. M., Mixed symmetric duality in nondifferentiable mathematical programming, European Journal of Operational Research, 181, 1-9 (2007). CrossRef
Mond, B., Second order duality for nonlinear programs, Opsearch, 11, 90-99 (1974).
Suneja, S. K., Lalita, C.S. and Khurana, S., Second order symmetric dual in multiobjective programming, European Journal of Operational Research, 144, 492-500 (2003). CrossRef
Thakur, G. K. and Priya, B., Second order duality for nondifferentiable multiobjective programming involving (Φ,Ï)-univexity, Kathmandu University Journal of Science, Engineering and Technology, 7 (1), 99-104 (2011).
Xu, Z., Mixed type duality in multiobjective programming problems, Journal of Mathematical Analysis and Applications, 198, 621-635 (1996). CrossRef
Yang, X. M., Teo, K. L. and Yang, X. Q., Mixed symmetric duality in nondifferentiable Mathematical programming, Indian Journal of Pure and Applied Mathematics, 34 (5), 805-815 (2003).
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