Opuscula Math. 34, no. 4 (), 665-682
http://dx.doi.org/10.7494/OpMath.2014.34.4.665
Opuscula Mathematica

# 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.
Keywords: multiobjective variational control problems, efficient solution, $$B$$-$$(p,r)$$-invex functions, optimality conditions, duality.
Mathematics Subject Classification: 65K10, 90C29, 26B25.