Optimising for most efficient lambda in Nelson Siegel factor

Hi, I hope you're well. I am currently writing Nelson Siegel optimisation code. Using the NS formula I'm just running an ordinary least squares regression using a fixed lambda of .7308.

However, i've found that this throws up a lot of problems when running against convex curves. I've tried varying teh lambda and this helps so now i want to run a loop that finds the optimal lambda for each yiled curve. I was thinking of using fminsearch but am unsure of how to define the function as I have no no fixed variable. Any help would be greatly appreciated.