How to optimise a complex function with five parameters ?

I would like to optimize the values of Johnson-Cook material model parameters(five in total) by comparing the experimental values of 3 variables(cutting force, thrust force and chip thickness) obtained from simulations. Which optimisation technique should be implemented? The parameters to be optimised are A, B, C, n, m(refer to the attached picture).

[Star Strider]

Are you (1) fitting data (so you have dependent data for ‘sigma’ and independent data for the two other variables) and estimating the other parameters, or are you (2) minimizing or maximizing ‘sigma’ for some combination of 3 variables?

[tarun sathapathi]

Hey. Thanks for replying. I'll fix few experimental conditions, assume initial values for A, B, C, n, m and use this formula to find 'sigma' which is further used to find forces and chip thickness. The objective function is to reduce the error between simulated and experimental values of forces and chip thickness. Based on this objective function, the code has to keep altering the values of A, B, C, n, m. I hope this answers your question.

[Star Strider]

Are you fitting ‘sigma’ directly (with experimental data for it as a dependent variable, and using experimental data for two independent variables) or are you actually fitting a more extensive set of equations?

I do not understand the notation in the equation you posted, or what your variables mean, since my background is not in that area (and I suspect that applies to most of us here). You have to explain what you are doing.