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**Primal hybrid variational formulation of an elliptic state equation incorporated into an optimal shape problem.**
*(English)*
Zbl 0874.49037

Neittaanmäki, P. (ed.), Proceedings of the workshop on optimization and optimal control held at Jyväskylä, Finland, 28.-29.9.1992. Jyväskylä: University of Jyväskylä, Department of Mathematics. Ber., Univ. Jyväskylä. 58, 31-40 (1993).

The goal of the contribution is to give a mathematical backing to a method applicable to certain optimal shape problems. There are different sensitivity analysis methods used in the field of optimal shape design. Generally speaking, we can distinguish two main approaches. The first analyses sensitivity of a discretized optimal shape problem. The second deals with the original (continuous) problem and a resulting sensitivity formula is approximated by a solution of a discrete state equation.

The latter approach may lead to considerable simple formulae. However, we have to expect a loss of accuracy of a computed gradient of a (smooth) cost functional. To reduce an error a suitable formulation of a state equation is desirable.

In the contribution the primal hybrid method is applied to a state equation. This enables us to fit demands of a sensitivity analysis used. Both existence and convergence results are presented. Details can be found in Kybernetika 29, No. 3, 231-248 (1993; Zbl 0805.49024).

For the entire collection see [Zbl 0778.00032].

The latter approach may lead to considerable simple formulae. However, we have to expect a loss of accuracy of a computed gradient of a (smooth) cost functional. To reduce an error a suitable formulation of a state equation is desirable.

In the contribution the primal hybrid method is applied to a state equation. This enables us to fit demands of a sensitivity analysis used. Both existence and convergence results are presented. Details can be found in Kybernetika 29, No. 3, 231-248 (1993; Zbl 0805.49024).

For the entire collection see [Zbl 0778.00032].

### MSC:

49Q10 | Optimization of shapes other than minimal surfaces |

49K20 | Optimality conditions for problems involving partial differential equations |