Second-Order Necessary Conditions in Pontryagin Form for Optimal Control Problems

J. Frédéric Bonnans; Xavier Dupuis; Laurent Pfeiffer

doi:10.1137/130923452

Second-Order Necessary Conditions in Pontryagin Form for Optimal Control Problems

SIAM Journal on Control and Optimization ◽

10.1137/130923452 ◽

2014 ◽

Vol 52 (6) ◽

pp. 3887-3916 ◽

Cited By ~ 10

Author(s):

J. Frédéric Bonnans ◽

Xavier Dupuis ◽

Laurent Pfeiffer

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Second Order ◽

Control Problems ◽

Second Order Necessary Conditions ◽

Pontryagin Form

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First- and second-order necessary conditions with respect to components for discrete optimal control problems

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2019.112342 ◽

2020 ◽

Vol 364 ◽

pp. 112342

Author(s):

Misir J. Mardanov ◽

Telman K. Melikov ◽

Samin T. Malik ◽

Kamran Malikov

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Second Order ◽

Control Problems ◽

Discrete Optimal Control ◽

Second Order Necessary Conditions

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Second Order Necessary Conditions and Sensitivity Relations for Optimal Control Problems on Riemannian Manifolds

2018 37th Chinese Control Conference (CCC) ◽

10.23919/chicc.2018.8483243 ◽

2018 ◽

Author(s):

Li Deng

Keyword(s):

Optimal Control ◽

Riemannian Manifolds ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Second Order ◽

Control Problems ◽

Second Order Necessary Conditions

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Second order necessary conditions for optimal control problems with control and integral constraints

10.1109/cdc.1985.268560 ◽

1985 ◽

Author(s):

M. Kazemi-dehkordi ◽

Kang Shin

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Second Order ◽

Control Problems ◽

Integral Constraints ◽

Second Order Necessary Conditions

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Second Order Necessary Conditions for Optimal Control Problems of Stochastic Evolution Equations

SIAM Journal on Control and Optimization ◽

10.1137/20m1343762 ◽

2021 ◽

Vol 59 (4) ◽

pp. 2924-2954

Author(s):

Qi Lü ◽

Haisen Zhang ◽

Xu Zhang

Keyword(s):

Optimal Control ◽

Evolution Equations ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Second Order ◽

Control Problems ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

Second Order Necessary Conditions

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Second order necessary conditions for endpoints-constrained optimal control problems on Riemannian manifolds

Journal of Differential Equations ◽

10.1016/j.jde.2020.10.005 ◽

2021 ◽

Vol 272 ◽

pp. 854-910

Author(s):

Li Deng ◽

Xu Zhang

Keyword(s):

Optimal Control ◽

Riemannian Manifolds ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Second Order ◽

Control Problems ◽

Constrained Optimal Control ◽

Second Order Necessary Conditions

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First and Second Order Necessary Conditions for Stochastic Optimal Control Problems

Applied Mathematics & Optimization ◽

10.1007/s00245-012-9162-4 ◽

2012 ◽

Vol 65 (3) ◽

pp. 403-439 ◽

Cited By ~ 21

Author(s):

J. Frédéric Bonnans ◽

Francisco J. Silva

Keyword(s):

Optimal Control ◽

Stochastic Optimal Control ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Second Order ◽

Control Problems ◽

Second Order Necessary Conditions

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Strong Local Minimizers in Optimal Control Problems with State Constraints: Second-Order Necessary Conditions

SIAM Journal on Control and Optimization ◽

10.1137/17m1160604 ◽

2018 ◽

Vol 56 (3) ◽

pp. 2353-2376 ◽

Cited By ~ 7

Author(s):

Hélène Frankowska ◽

Nikolai P. Osmolovskii

Keyword(s):

Optimal Control ◽

State Constraints ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Second Order ◽

Control Problems ◽

Local Minimizers ◽

Second Order Necessary Conditions

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Algorithms for Nonlinear Optimal Control Problems Based on the First and Second Order Necessary Conditions

Journal of Mathematical Sciences ◽

10.1007/s10958-019-04293-y ◽

2019 ◽

Vol 239 (2) ◽

pp. 185-196

Author(s):

A. I. Tyatyushkin ◽

T. S. Zarodnyuk ◽

A. Yu. Gornov

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Nonlinear Optimal Control ◽

Second Order ◽

Control Problems ◽

Second Order Necessary Conditions

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Second order necessary conditions for optimal control problems of stochastic evolution equations

2016 35th Chinese Control Conference (CCC) ◽

10.1109/chicc.2016.7553759 ◽

2016 ◽

Cited By ~ 1

Author(s):

Qi Lu

Keyword(s):

Optimal Control ◽

Evolution Equations ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Second Order ◽

Control Problems ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

Second Order Necessary Conditions

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Second-Order Necessary Conditions for Stochastic Optimal Control Problems

SIAM Review ◽

10.1137/17m1148773 ◽

2018 ◽

Vol 60 (1) ◽

pp. 139-178 ◽

Cited By ~ 1

Author(s):

Haisen Zhang ◽

Xu Zhang

Keyword(s):

Optimal Control ◽

Stochastic Optimal Control ◽

Optimal Control Problems ◽

Necessary Conditions ◽

Second Order ◽

Control Problems ◽

Second Order Necessary Conditions

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