Implicit function. Controllability and perturbation of optimal control problems (Q2037690)

An implicit function theorem is proved in the case where the implicit function is required to belong to a prescribed convex set. The result is applied to prove some stability results for optimal control problems under convexification of the dynamics and perturbation of a state constraint. In particular, the absence of infimum gap under convexification and perturbation for control problems with a class of endpoint state constraints is proved by requiring that a reference trajectory does not admit a set of dual variables satisfying a nondegenerate version of Pontryagin Maximum principle.