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.
On the convexity of the value function for a class of nonconvex variational problems: existence and optimality conditions
MASTROENI, GIANDOMENICO
2014-01-01
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
On the convexity.pdf
accesso aperto
Tipologia:
Versione finale editoriale
Licenza:
Creative commons
Dimensione
243.4 kB
Formato
Adobe PDF
|
243.4 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.