Parametric approach to multitime multiobjective fractional variational problems under (F,ρ)-convexity
Tadeusz Antczak, Ariana Pitea · Optimal Control Applications and Methods · 2015
In this paper, we consider a multitime multiobjective fractional variational problem of minimizing a vector of quotients of path-independent curvilinear integral functionals subject to certain partial differential equations and inequations. Using the so-called parametric approach, we establish necessary and sufficient optimality conditions for the considered class of multitime multiobjective fractional variational problems under both (F,ρ)-convexity and generalized (F,ρ)-convexity. Further, the parametric multiobjective variational dual problem is formulated for the considered multitime multiobjective fractional variational problem, and several duality results are established under (generalized) (F,ρ)-convexity. Copyright © 2015 John Wiley & Sons, Ltd.