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