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April  2011, 29(2): 505-522. doi: 10.3934/dcds.2011.29.505

Lipschitz continuity of optimal control and Lagrange multipliers in a problem with mixed and pure state constraints

Maria do Rosário de Pinho 1, and  Ilya Shvartsman 2,

1. 

Faculdade de Engenharia da Universidade do Porto, Department of Electrical Engineering and Computers, Porto, Portugal
2. 

Department of Mathematics and Computer Science, Penn State Harrisburg, Middletown, PA 17057, United States

Received  September 2009 Revised  April 2010 Published  October 2010

In this paper we report conditions ensuring Lipschitz continuity of optimal control and Lagrange multipliers for a dynamic optimization problem with inequality pure state and mixed state-control constraints.
Keywords: Lipschitz control, necessary optimality conditions, Optimal control, regularity..
Mathematics Subject Classification: Primary: 49K15, 49K4.
Citation: 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 & Continuous Dynamical Systems, 2011, 29 (2) : 505-522. doi: 10.3934/dcds.2011.29.505
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show all references

References:
[1]

Ann. I. H. Poincaré - Analyse Non Linéaire, 26 (2009), 561-598.  Google Scholar

[2]

Springer-Verlag, New York, 2000. Google Scholar

[3]

Comp. Math. and Modeling, 4 (1993), 364-377. doi: doi:10.1007/BF01128760.  Google Scholar

[4]

SIAM J. Control and Optimization, 42 (2003), 1727-1744. doi: doi:10.1137/S0363012902404711.  Google Scholar

[5]

SIAM J. Control and Optimization, 17 (1979), 321-338. doi: doi:10.1137/0317026.  Google Scholar

[6]

Arch. Auto. i Telemech., 23 (1978), 227-241.  Google Scholar

[7]

Optimization, 52 (2003), 75-91. doi: doi:10.1080/0233193021000058940.  Google Scholar

[8]

Moscow State University Press, 2004. Available online at http://www.milyutin.ru/book.html. Google Scholar

[9]

J. Math. Anal. Appl., 45 (1974), 506-511. doi: doi:10.1016/0022-247X(74)90089-4.  Google Scholar

[10]

Mathematics of Operations Research, 5 (1980), 43-62. doi: doi:10.1287/moor.5.1.43.  Google Scholar

[11]

Nonlinear Analysis: Theory, Methods and Applications, 65 (2006), 448-474.  Google Scholar

[12]

Birkhäuser, Boston, 2000. Google Scholar

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