European Journal of Applied Mathematics

A survey on level set methods for inverse problems and optimal design

a1 Industrial Mathematics Institute, Johannes Kepler Universität, Altenbergerstr. 69, 4040 Linz, Austria email
a2 Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA 90095, USA email:

Article author query
burger m   [Google Scholar] 
osher js   [Google Scholar] 


The aim of this paper is to provide a survey on the recent development in level set methods in inverse problems and optimal design. We give introductions on the general features of such problems involving geometries and on the general framework of the level set method. In subsequent parts we discuss shape sensitivity analysis and its relation to level set methods, various approaches on constructing optimization algorithms based on the level set approach, and special tools needed for the application of level set based optimization methods to ill-posed problems. Furthermore, we provide a review on numerical methods important in this context, and give an overview of applications treated with level set methods. Finally, we provide a discussion of the most challenging and interesting open problems in this field, that might be of interest for scientists who plan to start future research in this field.

(Received January 29 2004)
(Revised July 23 2004)


1 This paper was written while the first author was on leave at Department of Mathematics, UCLA