Duality for multiobjective variational control problems with $$(\Phi , \rho )$$ ( Φ , ρ ) -invexity

Abstract

In this paper, Mond-Weir and Wolfe type duals for multiobjective variational control problems are formulated. Several duality theorems are established relating efficient solutions of the primal and dual multiobjective variational control problems under ( , ρ)-invexity. The results generalize a number of duality results previously established for multiobjective variational control problems under other generalized convexity assumptions.

On a Dual Pair of Multiobjective Interval-Valued Variational Control Problems

“…Ahmad and Sharma [6] obtained sufficient conditions of optimality and formulated Wolfe and Mond-Weir duals for a class of multiobjective variational control problems. Further, Antczak [7] established Mond-Weir and Wolfe type duals for multiobjective variational control problems under (Φ, ρ)-invexity. Recently, Mititelu and Treanţȃ [8] formulated and proved efficiency conditions in vector control problems governed by multiple integrals.…”

On optimality and duality in interval-valued variational problem withB-(p,r)-invexity

“…Bector and Husain [16] extended the concept of duality used in vector optimization problem to variational problem. Thereafter, many researchers derived duality relations for multiobjective problem under generalized invexity assumptions [9,[16][17][18][19][20][21][22][23][24].…”

“…They are of interest as they play an important role in analysing the behaviour of original problem and also helps in obtaining an optimal solution. Antczak and Jiménez [19,20] established optimality conditions and duality results for a multiobjective variational problem utilizing B-(p, r)-invexity and (φ, ρ)-invexity. Bhatia and Mehra [22] derived optimality and duality results under generalized B-invexity assumptions.…”