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Paper IPM / M / 11242  


Abstract:  
In (ZAA J. Anal. Appl., Vol. 16, No. 1, pp. 143155) we introduced a method to determine the optimal domains for elliptic optimalshape design problems in polar coordinates. However, the same problem in cartesian coor�dinates, which are more applicable, is found to be much harder, therefore we had to develop a new approach for these designs. Herein, the unknown domain is divided into a fixed and a variable part and the optimal pair of the domain and its optimal control, is characterized in two stages. Firstly, the optimal con�trol for the each given domain is determined by changing the problem into a measuretheoretical one, replacing this with an infinite dimensional linear programming problem and approximating schemes; then the nearly optimal control function is characterized. Therefore a function that offers the optimal value of the objective function for a given domain, is defined. In the second stage, by applying a standard optimization method, the global minimizer pair will be obtained. Some numerical examples are also given.
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