@misc{Osmolovskii_Nikolai_Simple_2013, author={Osmolovskii, Nikolai}, copyright={Creative Commons Attribution BY 4.0 license}, journal={Raport Badawczy = Research Report}, address={Warszawa}, howpublished={online}, year={2013}, publisher={Instytut Badań Systemowych. Polska Akademia Nauk}, publisher={Systems Research Institute. Polish Academy of Sciences}, language={eng}, abstract={The paper considers optimal control problems with initial-final state equality and inequality constraints and moxed state-control equality constraints given by smooth functions. The mixed constraints satisfy the regularity assumption of linear independence of gradients with respect to the control. Simple proofs of second-order necessary conditions of Pontryagin minimum for broken extremals in these problems are presented.}, type={Text}, title={Simple Proofs of Second order Necessary Conditions for Broken Extremals}, URL={http://rcin.org.pl./Content/104670/PDF/RB-2013-03.pdf}, keywords={Optimal control, Optymalna kontrola, Warunek konieczny optymalności, Necessary optimality conditions}, }