Systems Research Institute, ul. Newelska 6, 01-447 Warszawa, Poland
Politechnika Radomska, ul. Malczewskiego 20A, 26-600 Radom, Poland
University of Natural Sciences and Humanities in Siedlce, ul. 3 Maja 54, 08-110 Siedlce, Poland. email@example.com
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.
(Received November 28 2009)
(Revised November 27 2010)
(Online publication June 22 2011)
Mathematics Subject Classification: