November  2012, 11(6): 2473-2485. doi: 10.3934/cpaa.2012.11.2473

On dual dynamic programming in shape control

1. 

University of Lodz, Faculty of Math & Computer Sciences, Banacha 22, 90-238 Lodz, Poland

2. 

Institut Elie Cartan, UMR 7502 (Nancy Université, CNRS, INRIA), Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre-lès-Nancy, Cedex

Received  June 2010 Revised  November 2010 Published  April 2012

We propose a new method for analysis of shape optimization problems. The framework of dual dynamic programming is introduced for a solution of the problems. The shape optimization problem for a linear elliptic boundary value problem is formulated in terms of characteristic functions which define the suport of control. The optimal solution of such a problem can be obtained by solving the sufficient optimality conditions.
Citation: Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure & Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473
References:
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Nonlinear Anal., 42 (2000), Ser. A: Theory Methods, 871-886. doi: 10.1016/S0362-546X(99)00134-0.  Google Scholar

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Comput. Optim. Appl., 42 (2009), 443-470. doi: 10.1007/s10589-007-9133-x.  Google Scholar

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Int. J. Numer. Anal. Model., 5 (2008), 331-351.  Google Scholar

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Proceedings of the American Mathematical Society, 116 (1992), 1089-1096. doi: 10.1090/S0002-9939-1992-1102860-3.  Google Scholar

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SIAM J. Control Optim., 47 (2008), 92-110. doi: 10.1137/050644008.  Google Scholar

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Systems & Control Letters, 58 (2009), 136-140. doi: 10.1016/j.sysconle.2008.08.007.  Google Scholar

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Springer - Verlag, 1992. doi: 10.1007/978-3-642-58106-9.  Google Scholar

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Inverse problems, 15, (1999), 123-134. doi: 10.1088/0266-5611/15/1/016.  Google Scholar

show all references

References:
[1]

Nonlinear Anal., 42 (2000), Ser. A: Theory Methods, 871-886. doi: 10.1016/S0362-546X(99)00134-0.  Google Scholar

[2]

Princeton University Press, Princeton, 1957. doi: 10.1126/science.153.3731.34.  Google Scholar

[3]

Advances in Design and Control, SIAM, 2001.  Google Scholar

[4]

Springer Verlag, New York, NY, 1975.  Google Scholar

[5]

Numer. Funct. Anal. Optim., 27 (2006), 279-289. doi: 10.1080/01630560600698160.  Google Scholar

[6]

Springer - Verlag, 2001.  Google Scholar

[7]

P. Hebrard and A. Henrot, Spillover phenomenon in the optimal locations of actuators,, SIAM J. Control Optim., 44 (): 349.  doi: 10.1016/S0167-6911(02)00265-7.  Google Scholar

[8]

Systems and Control Letters, 48 (2003), 199-209.  Google Scholar

[9]

(French) Mathématiques et Applications 48, Springer, 2005.  Google Scholar

[10]

Comm. Pure Appl. Math., 39, (1986), 113-137. doi: 10.1002/cpa.3160390107.  Google Scholar

[11]

(French) Coll. Dir. Etudes et Recherches EDF, 57, Eyrolles, Paris, (1985) 319-369.  Google Scholar

[12]

Comput. Optim. Appl., 42 (2009), 443-470. doi: 10.1007/s10589-007-9133-x.  Google Scholar

[13]

Int. J. Numer. Anal. Model., 5 (2008), 331-351.  Google Scholar

[14]

Proceedings of the American Mathematical Society, 116 (1992), 1089-1096. doi: 10.1090/S0002-9939-1992-1102860-3.  Google Scholar

[15]

SIAM J. Control Optim., 47 (2008), 92-110. doi: 10.1137/050644008.  Google Scholar

[16]

Systems & Control Letters, 58 (2009), 136-140. doi: 10.1016/j.sysconle.2008.08.007.  Google Scholar

[17]

Springer - Verlag, 1992. doi: 10.1007/978-3-642-58106-9.  Google Scholar

[18]

Inverse problems, 15, (1999), 123-134. doi: 10.1088/0266-5611/15/1/016.  Google Scholar

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