Abstract
In this paper, we extend the Mishra, Rueda and Giorgi generalized V-univexity type I, defined for multiobjective programming, to multiobjective variational programming problems and we derive various sufficient optimality conditions and mixed type duality results under generalized V-univexity type I conditions.
Similar content being viewed by others
References
Chinchuluun, A., Pardalos, P.M.: Multiobjective programming problems under generalized convexity. In: Torn, A., Zilinskas, J. (eds.) Models and Algorithms for Global Optimization, pp. 3–20. Springer, Berlin (2006)
Mond, B., Hanson, M.A.: Duality for variational problems. J. Math. Anal. Appl. 18, 355–364 (1967)
Mishra, S.K., Wang, S.Y., Lai, K.K.: V-Invex Functions and Vector Optimization. Springer Optimization and Its Applications, vol. 14. Springer, Berlin (2008)
Bector, C.R., Husain, I.: Duality for multiobjective variational problems. J. Math. Anal. Appl. 166, 214–229 (1992)
Aghezzaf, B., Hachimi, M.: Generalized invexity and duality in multiobjective programming problems. J. Glob. Optim. 18, 91–101 (2000)
Aghezzaf, B., Hachimi, M.: Sufficiency and duality in multiobjective variational problems with generalized type I functions. J. Glob. Optim. 34, 191–218 (2006)
Nahak, C., Nanda, C.: Duality for multiobjective variational problems with invexity. Optimization 36, 235–248 (1996)
Mond, B., Chandra, S., Husain, I.: Duality for variational problems with invexity. J. Math. Anal. Appl. 134, 322–328 (1988)
Bhatia, D., Kumar, P.: Duality for multiobjective variational problems with B-vex functions. Optimization 36, 347–360 (1996)
Bhatia, D., Mehra, A.: Optimality conditions and duality for multiobjective variational problems with generalized B-invexity. J. Math. Anal. Appl. 234, 341–360 (1999)
Mukherjee, R.N., Purnachandra Rao, C.: Mixed type duality for multiobjective variational problems. J. Math. Anal. Appl. 252, 571–586 (2000)
Aghezzaf, B., Khazafi, K.: Sufficient optimality conditions and duality in multiobjective variational programming problems with generalized b-invexity. J. Control Cyber. 33, 1–14 (2004)
Mishra, S.K., Rueda, N.G., Giorgi, G.: Multiobjective programming under generalized type I univexity. An. Univ. Bucur. Mat. 52, 207–224 (2003)
Valentine, F.A.: The Problem of Lagrange with Differentiable Inequalities as Added Side Constraints, Contribution to the Calculus of Variation, 1933–1937. University of Chicago Press, Chicago (1937), pp. 407–448
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by P.M. Pardalos.
The authors thank the referee for many valuable comments and helpful suggestions.
Rights and permissions
About this article
Cite this article
Khazafi, K., Rueda, N. Multiobjective Variational Programming under Generalized Type I Univexity. J Optim Theory Appl 142, 363–376 (2009). https://doi.org/10.1007/s10957-009-9526-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10957-009-9526-3