Fabián Flores-Bazán, Abderrahim Jourani, Giandomenico Mastroeni:
On the convexity of the value function for a class of nonconvex variational problems: existence and optimality conditions
In this paper we study a class of perturbed constrained nonconvex variational problems. 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, 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
This preprint gave rise to the following definitive publication(s):
Fabián FLORES-BAZáN, Abderrahim JOURANI, Giandomenico MASTROENI: On the convexity of the value function for a class of nonconvex variational problems: Existence and optimality conditions. SIAM Journal on Control and Optimization, vol. 52, 6, pp. 3673-3693, (2014).