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Numerical methods for shape identification problems. (English) Zbl 0876.65048
The problem considered here is to minimize a standard quadratic functional, the optimization parameter being an inclusion in the domain. The authors prove an existence result for \(n=2\), and then discuss first and second optimality conditions based on the technique of material derivative. The numerical method involves boundary elements, the Lagrange-Newton method and a penalty technique. Some numerical examples are discussed.

65K10 Numerical optimization and variational techniques
49K20 Optimality conditions for problems involving partial differential equations
49M15 Newton-type methods
49M30 Other numerical methods in calculus of variations (MSC2010)