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

Nikolai P. Osmolovskii

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 2, page 452-482
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Osmolovskii, Nikolai P.. "Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints." ESAIM: Control, Optimisation and Calculus of Variations 18.2 (2012): 452-482. <http://eudml.org/doc/221921>.

@article{Osmolovskii2012,
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. },
author = {Osmolovskii, Nikolai P.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Pontryagin’s principle; critical cone; quadratic form; second order sufficient condition; quadratic growth; Hoffman’s error bound; Pontryagin's principle; Hoffman's error bound},
language = {eng},
month = {7},
number = {2},
pages = {452-482},
publisher = {EDP Sciences},
title = {Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints},
url = {http://eudml.org/doc/221921},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Osmolovskii, Nikolai P.
TI - Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/7//
PB - EDP Sciences
VL - 18
IS - 2
SP - 452
EP - 482
AB - 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.
LA - eng
KW - Pontryagin’s principle; critical cone; quadratic form; second order sufficient condition; quadratic growth; Hoffman’s error bound; Pontryagin's principle; Hoffman's error bound
UR - http://eudml.org/doc/221921
ER -

References

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