Second-order sufficient conditions of a bounded strong minimum are derived for optimalcontrol problems of ordinary differential equations with initial-final state constraintsof equality and inequality type and control constraints of inequality type. The conditionsare stated in terms of quadratic forms associated with certain tuples of Lagrangemultipliers. Under the assumption of linear independence of gradients of active controlconstraints they guarantee the bounded strong quadratic growth of the so-called “violationfunction”. Together with corresponding necessary conditions they constitute a no-gap pairof conditions.
