Sufficient Efficiency Conditions for Vector Ratio Problem on the Second-Order Jet Bundle

Motivated by its possible applications in mechanics and mechanical engineering, in our previous published work (Pitea and Postolache, 2011), we initiated an optimization theory for the second-order jet bundle. We considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multitime multiobjective variational problems, subject to PDE and/or PDI constraints. Within this framework, we introduced necessary optimality conditions. As natural continuation of these results, the present work introduces a study of sufficient efficiency conditions.