Strongly motivated by its possible applications in Mechanics, in our previous work (Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 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 multi-time multi-objective variational problems, subject to PDE and/or PDI constraints. Within this framework, we introduced necessary conditions. As natural continuation of our results in Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011), the present work introduces a study of sufficient efficiency conditions. While the background in Sect. 2 is introductory, the theory in Sect. 3 is new as a whole, containing our results.
Lagrange 1-form density Multi-objective variational problem Quasiinvexity Efficiency
Hachimi M., Aghezzaf B.: Sufficiency and duality in differentiable multiobjective programming involving generalized type I functions. J. Math. Anal. Appl. 296, 382–392 (2004)MathSciNetMATHCrossRefGoogle Scholar