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

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

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

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topOsmolovskii, 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 -

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