A class of multiobjective variational control and multiobjective fractional variational control problems is considered, and the duality results are formulated. Under pseudoinvexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved.
C. R. Bector, S. Chandra, and C. Singh, “Duality in multiobjective fractional programming,” in International Workshop on Generalized Concavity, Fractional Programming and Economic Application, pp. 1–15, Italy, 1988.
View at: Google ScholarC. R. Bector and I. H. Husain, “Duality for multiobjective variational problems,” Journal of Mathematical Analysis and Applications, vol. 166, no. 1, pp. 214–229, 1992.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Chandra, B. D. Craven, and I. H. Husain, “A class of nondifferentiable continuous programming problems,” Journal of Mathematical Analysis and Applications, vol. 107, no. 1, pp. 122–131, 1985.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetB. D. Craven, “Lagrangean conditions and quasiduality,” Bulletin of the Australian Mathematical Society, vol. 16, no. 3, pp. 325–339, 1977.
View at: Google Scholar | Zentralblatt MATH | MathSciNetB. D. Craven, “Lagrangian conditions, vector minimization and local duality,” Research Report 37, Department of Mathematics, University of Melbourne, Melbourne, 1980.
View at: Google ScholarM. A. Hanson, “Bounds for functionally convex optimal control problems,” Journal of Mathematical Analysis and Applications, vol. 8, no. 1, pp. 84–89, 1964.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. K. Mishra and R. N. Mukherjee, “Duality for multiobjective fractional variational problems,” Journal of Mathematical Analysis and Applications, vol. 186, no. 3, pp. 711–725, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetB. Mond and M. A. Hanson, “Duality for variational problems,” Journal of Mathematical Analysis and Applications, vol. 18, no. 2, pp. 355–364, 1967.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetC. Nahak and S. Nanda, “Duality for multiobjective variational problems with invexity,” Optimization, vol. 36, no. 3, pp. 235–248, 1996.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetC. Nahak and S. Nanda, “On efficiency and duality for multiobjective variational control problems with -convexity,” Journal of Mathematical Analysis and Applications, vol. 209, no. 2, pp. 415–434, 1997.
View at: Google Scholar | Zentralblatt MATH | MathSciNet