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Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints

Published online by Cambridge University Press:  22 June 2011

Nikolai P. Osmolovskii
Nikolai P. Osmolovskii*
Affiliation:
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. osmolovski@uph.edu.pl
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Abstract

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.

Keywords

Pontryagin’s principlecritical conequadratic formsecond order sufficient conditionquadratic growthHoffman’s error bound
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 2 , April 2012 , pp. 452 - 482
Copyright
© EDP Sciences, SMAI, 2011

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