Optimal control and invexity

For a constrained minimization problem in infinite dimensions, in particular an optimal control problem, the attainment of a minimum follows if necessary Lagrangian conditions—Karush-Kuhn-Tucker or equivalently Pontryagin—are solvable, provided that a suitable invex hypothesis holds. Duality results are also obtained, where part of the constraint system describes a curved (hyper-) surface, and the invex property is assumed on that surface.