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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 1, 1999, pp. 143–155
DOI: 10.4171/ZAA/874

Published online: 1999-03-31

Global Solution of Optimal Shape Design Problems

A. Fakharzadeh[1] and J.E. Rubio[2]

(1) Shahid Chamran University, Ahwaz, Iran
(2) University of Leeds, UK

We consider optimal shape design problems defined by pairs of geometrical elements and control functions associated with linear or nonlinear elliptic equations. First, necessary conditions are illustrated in a variational form. Then by applying an embedding process, the problem is extended into a measure-theoretical one, which has some advantages. The theory suggests the development of a computational method consisting of the solution of a finite-dimensional linear programming problem. Nearly optimal shapes and related controls can thus be constructed. Two examples are also given.

Keywords: Embedding methods, optimal shape design, Radon measures, linear programming, optimal shape, optimal control, elliptic equations

Fakharzadeh A., Rubio J.E.: Global Solution of Optimal Shape Design Problems. Z. Anal. Anwend. 18 (1999), 143-155. doi: 10.4171/ZAA/874