Geodesic
Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 2, pp. 452-482

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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.

DOI : 10.1051/cocv/2011101
Classification : 49K15
Keywords: Pontryagin's principle, critical cone, quadratic form, second order sufficient condition, quadratic growth, Hoffman's error bound 
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     author = {Osmolovskii, Nikolai P.},
     title = {Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {452--482},
     publisher = {EDP-Sciences},
     volume = {18},
     number = {2},
     year = {2012},
     doi = {10.1051/cocv/2011101},
     mrnumber = {2954634},
     zbl = {1246.49017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011101/}
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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, Tome 18 (2012) no. 2, pp. 452-482. doi: 10.1051/cocv/2011101

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