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.