Symmetric duality with (p,r) ― ρ ― (η,θ)-invexity

作者: P. Mandal , C. Nahak

DOI: 10.1016/J.AMC.2011.02.068

关键词:

摘要: Abstract In this paper we introduce a new type of generalized invex function, called (p, r) − ρ − (η, θ)-invex function and study symmetric duality results under these assumptions. our the nonnegative orthants for constraints are replaced by closed convex cones their polars. We establish weak strong theorems (p, r) − ρ − (η, θ)-invexity assumptions dual problems. also give many examples to justify results.

参考文章(13)
C. Nahak, On multiobjective generalized symmetric dual programs withρ − (η, θ)-invexity Korean Journal of Computational & Applied Mathematics. ,vol. 5, pp. 707- 713 ,(1998) , 10.1007/BF03008893
Do Sang Kim, Won Jung Lee, Generalized symmetric duality for multiobjective variational problems with invexity Journal of Mathematical Analysis and Applications. ,vol. 234, pp. 147- 164 ,(1999) , 10.1006/JMAA.1999.6344
Tadeusz Antczak, A class of B-(p,r)-invex functions and mathematical programming Journal of Mathematical Analysis and Applications. ,vol. 286, pp. 187- 206 ,(2003) , 10.1016/S0022-247X(03)00469-4
C. Nahak, S. Nanda, Symmetric duality with pseudo-invexity in variational problems European Journal of Operational Research. ,vol. 122, pp. 145- 150 ,(2000) , 10.1016/S0377-2217(99)00067-3
T.R. Gulati, Geeta, On some symmetric dual models in multiobjective programming Applied Mathematics and Computation. ,vol. 215, pp. 380- 383 ,(2009) , 10.1016/J.AMC.2009.05.032
George Dantzig, E. Eisenberg, Richard Cottle, Symmetric dual nonlinear programs. Pacific Journal of Mathematics. ,vol. 15, pp. 809- 812 ,(1965) , 10.2140/PJM.1965.15.809
Tadeusz Antczak, (p,r)-Invex Sets and Functions Journal of Mathematical Analysis and Applications. ,vol. 263, pp. 355- 379 ,(2001) , 10.1006/JMAA.2001.7574
M. S. Bazaraa, J. J. Goode, On Symmetric Duality in Nonlinear Programming Operations Research. ,vol. 21, pp. 1- 9 ,(1973) , 10.1287/OPRE.21.1.1
S. Nanda, L.N. Das, Pseudo-invexity and symmetric duality in nonlinear fractional programming European Journal of Operational Research. ,vol. 73, pp. 577- 582 ,(1994) , 10.1016/0377-2217(94)90255-0