Opuscula Math. 34, no. 4 (2014), 665-682
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.