On cost function transformations for the reduction of uncertain model parameters' impact towards the optimal solutions

Uncertainties affect the accuracy of nonlinear static or dynamic optimization and inverse problems. The propagation of uncertain model parameters towards the optimal problem solutions can be assessed in a deterministic or stochastic way using Monte Carlo based techniques and efficient spectral collocation and Galerkin projection methods. This paper presents cost function transformations for reducing the impact of uncertain model parameters towards the optimal solutions. We assess the consistency of the methodology by determining sufficient conditions on the cost function transformations and apply the methodology on several test functions.