A better calibration method available?

i'm facing a new and interesting task: We are calculating a time series of (hypothetical) behavioral portfolios, for which i need a few parameters to calculate the portfolio's weights in each asset. I'm using an observed portfolio as starting point, from which i need to extract the implied utility parameters (in the case at hand the CPT utility as seen in my screeenshot). My idea is to find the parameters using a grid-search algorithm (as others such as Nelder-Mead don't reliably converge) and c