Sufficient optimality criteria and duality for multiobjective variational control problems with B-(p,r)-invex functions

Abstract

In this paper, we generalize the notion of $B$-$(p,r)$-invexity introduced by Antczak in [A class of $B$-$(p;r)$-invex functions and mathematical programming, J. Math. Anal. Appl. 286 (2003), 187–206] for scalar optimization problems to the case of a multiobjective variational programming control problem. For such nonconvex vector optimization problems, we prove sufficient optimality conditions under the assumptions that the functions constituting them are $B$-$(p,r)$-invex. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem in the sense of Mond-Weir is given and several duality results are established under $B$-$(p,r)$-invexity.