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Finite difference approximation for stochastic optimal stopping problems with delays
A nonsmooth Newton's method for discretized optimal control problems with state and control constraints
1.  School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom 
2.  Department of Mathematics, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany 
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Md. Haider Ali Biswas, Maria do Rosário de Pinho. A nonsmooth maximum principle for optimal control problems with state and mixed constraints  convex case. Conference Publications, 2011, 2011 (Special) : 174183. doi: 10.3934/proc.2011.2011.174 
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Huaiqiang Yu, Bin Liu. Pontryagin's principle for local solutions of optimal control governed by the 2D NavierStokes equations with mixed controlstate constraints. Mathematical Control and Related Fields, 2012, 2 (1) : 6180. doi: 10.3934/mcrf.2012.2.61 
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Eduardo Casas, Fredi Tröltzsch. Sparse optimal control for the heat equation with mixed controlstate constraints. Mathematical Control and Related Fields, 2020, 10 (3) : 471491. doi: 10.3934/mcrf.2020007 
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Vincenzo Basco, Piermarco Cannarsa, Hélène Frankowska. Necessary conditions for infinite horizon optimal control problems with state constraints. Mathematical Control and Related Fields, 2018, 8 (3&4) : 535555. doi: 10.3934/mcrf.2018022 
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Luís Tiago Paiva, Fernando A. C. C. Fontes. Adaptive timemesh refinement in optimal control problems with state constraints. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 45534572. doi: 10.3934/dcds.2015.35.4553 
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Theodore TachimMedjo. Optimal control of a twophase flow model with state constraints. Mathematical Control and Related Fields, 2016, 6 (2) : 335362. doi: 10.3934/mcrf.2016006 
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Matthias Gerdts, Martin Kunkel. Convergence analysis of Euler discretization of controlstate constrained optimal control problems with controls of bounded variation. Journal of Industrial and Management Optimization, 2014, 10 (1) : 311336. doi: 10.3934/jimo.2014.10.311 
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Alexander Tyatyushkin, Tatiana Zarodnyuk. Numerical method for solving optimal control problems with phase constraints. Numerical Algebra, Control and Optimization, 2017, 7 (4) : 481492. doi: 10.3934/naco.2017030 
[9] 
Matthias Gerdts, Stefan Horn, SvenJoachim Kimmerle. Line search globalization of a semismooth Newton method for operator equations in Hilbert spaces with applications in optimal control. Journal of Industrial and Management Optimization, 2017, 13 (1) : 4762. doi: 10.3934/jimo.2016003 
[10] 
Maria do Rosário de Pinho, Ilya Shvartsman. Lipschitz continuity of optimal control and Lagrange multipliers in a problem with mixed and pure state constraints. Discrete and Continuous Dynamical Systems, 2011, 29 (2) : 505522. doi: 10.3934/dcds.2011.29.505 
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Elimhan N. Mahmudov. Optimal control of second order delaydiscrete and delaydifferential inclusions with state constraints. Evolution Equations and Control Theory, 2018, 7 (3) : 501529. doi: 10.3934/eect.2018024 
[12] 
Yuefen Chen, Yuanguo Zhu. Indefinite LQ optimal control with process state inequality constraints for discretetime uncertain systems. Journal of Industrial and Management Optimization, 2018, 14 (3) : 913930. doi: 10.3934/jimo.2017082 
[13] 
Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navierstokes equations with state constraints. Evolution Equations and Control Theory, 2022, 11 (2) : 347371. doi: 10.3934/eect.2020110 
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Xiaojiao Tong, Felix F. Wu, Yongping Zhang, Zheng Yan, Yixin Ni. A semismooth Newton method for solving optimal power flow. Journal of Industrial and Management Optimization, 2007, 3 (3) : 553567. doi: 10.3934/jimo.2007.3.553 
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T. Tachim Medjo. On the Newton method in robust control of fluid flow. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 12011222. doi: 10.3934/dcds.2003.9.1201 
[16] 
Xiaojiao Tong, Shuzi Zhou. A smoothing projected Newtontype method for semismooth equations with bound constraints. Journal of Industrial and Management Optimization, 2005, 1 (2) : 235250. doi: 10.3934/jimo.2005.1.235 
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Shuang Chen, LiPing Pang, Dan Li. An inexact semismooth Newton method for variational inequality with symmetric cone constraints. Journal of Industrial and Management Optimization, 2015, 11 (3) : 733746. doi: 10.3934/jimo.2015.11.733 
[18] 
Piermarco Cannarsa, Hélène Frankowska, Elsa M. Marchini. On Bolza optimal control problems with constraints. Discrete and Continuous Dynamical Systems  B, 2009, 11 (3) : 629653. doi: 10.3934/dcdsb.2009.11.629 
[19] 
Mikhail Gusev. On reachability analysis for nonlinear control systems with state constraints. Conference Publications, 2015, 2015 (special) : 579587. doi: 10.3934/proc.2015.0579 
[20] 
M. Arisawa, P.L. Lions. Continuity of admissible trajectories for state constraints control problems. Discrete and Continuous Dynamical Systems, 1996, 2 (3) : 297305. doi: 10.3934/dcds.1996.2.297 
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