# American Institute of Mathematical Sciences

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
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