ON THE CONVEXITY OF THE VALUE FUNCTION FOR A CLASS OF NONCONVEX VARIATIONAL PROBLEMS: EXISTENCE AND OPTIMALITY CONDITIONS
| Affiliation auteurs | !!!! Error affiliation !!!! |
| Titre | ON THE CONVEXITY OF THE VALUE FUNCTION FOR A CLASS OF NONCONVEX VARIATIONAL PROBLEMS: EXISTENCE AND OPTIMALITY CONDITIONS |
| Type de publication | Journal Article |
| Year of Publication | 2014 |
| Auteurs | Flores-Bazan F., Jourani A., Mastroeni G. |
| Journal | SIAM JOURNAL ON CONTROL AND OPTIMIZATION |
| Volume | 52 |
| Pagination | 3673-3693 |
| Type of Article | Article |
| ISSN | 0363-0129 |
| Mots-clés | existence of minima, Hamiltonian, local minima, Lyapunov theorem, nonconvex variational problems, strong duality |
| Résumé | In this paper we study a class of perturbed constrained nonconvex variational problems depending on either time/state or time/state's derivative variables. Its (optimal) value function is proved to be convex and then several related properties are obtained. Existence, strong duality results, and necessary/sufficient optimality conditions are established. Moreover, via a necessary optimality condition in terms of Mordukhovich's normal cone, it is shown that local minima are global. Such results are given in terms of the Hamiltonian function. Finally various examples are exhibited showing the wide applicability of our main results. |
| DOI | 10.1137/14096877X |