Efficiency for variational control problems on Riemann manifolds with geodesic quasiinvex curvilinear integral functionals

Abstract

In this paper, we formulate and prove necessary and sufficient conditions of geodesic efficiency associated with a new class of multiobjective fractional variational control problems governed by geodesic quasiinvex path-independent curvilinear integral functionals and mixed constraints involving first order PDE of m-flow type. Under $$ \displaystyle (\rho , b) $$ -geodesic quasiinvexity assumptions, by using the new notion of (normal) geodesic efficient solution, we set sufficient conditions of geodesic efficiency for a feasible solution in the considered variational control problems.