Incomplete sensitivities and cost function reformulation leading to multi‐criteria investigation of inverse problems

This paper deals with the application of typical minimization methods based on dynamical systems to the solution of a characteristic inverse problem. The state equation is based on the Burgers equation. The control is meant to achieve a prescribed state distribution and a given shock location. We show how to use incomplete sensitivities during the minimization process. We also show through a redefinition of the cost function that a multi-criteria problem needs to be considered in inverse problems. This example shows that a correct definition of the minimization problem is crucial and needs to be studied before a direct application of brute force minimization approaches. Copyright © 2003 John Wiley & Sons, Ltd.