Second-order symmetric duality in multiobjective variational problems

Abstract

In this work, we introduce a pair of multiobjective second-order symmetric dual variational problems. Weak, strong, and converse duality theorems for this pair are established under the assumption of η-bonvexity/η-pseudobonvexity. At the end, the static case of our problems has also been discussed.

Robust Efficiency Conditions in Multiple-Objective Fractional Variational Control Problems

“…Research over the years has been progressively centered on multi-objective programming problem in various areas of mathematics such as optimal control theory, game theory, statistics, and finance. Numerous researchers have extensively examined the necessary and sufficient optimality conditions and important duality theorems for multi-objective control problems [1][2][3][4]. Mititelu and Treanţȃ [5] established necessary and sufficient efficiency conditions for multiobjective control problems that incorporate multiple integrals.…”

Symmetric duality in complex spaces over cones

“…Kaul and Sharma [18] presented a pair of differentiable symmetric dual nonlinear programs over special polyhedral cones and established weak duality theorem under convexity/concavity assumptions.They have also given an example to show that the strong duality theorem is not true. Some work on symmetric duality can be seen in [6,10,[12][13][14]25,26]. Mishra and Rueda [25], assuming F -convexity established duality theorems for Wolfe and Mond-Weir type first and second order symmetric dual programs in complex space.…”