Combining Multiobjective optimization with nonlinear least squares minimization

Hello

I am new to MATLAB and I am having problem with a multiobjective optimization problem. I have two nonlinear functions with several parameters which have to be fitted to experimental data, X, Y1, Y2:

f1(X,a,b,c) - the first function has three parameters a,b,and c that have to be determined by fitting the function to Y1.

f2(X,b,c,d) - the second function has three paramaters b,c, and d that have to be determined by fitting the function to Y2.

I have two objectives that uses least squares minimization as follows:

Objective 1: min (sum(f1 - Y1)^2) over all data points

Objective 2: min (sum(f2 - Y2)^2) over all data points

I need to find values of the four parameters (a, b, c, d) such that both the objectives are met. Only 3 out of the 4 parameters are in each objective. Also, there are upper and lower bounds on some of the parameters.

I am not sure how to implement this in MATLAB. Using nonlinear parameter estimation problems (such as 'lsqcurvefit', 'lsqnonlin', 'fmincon'), how can I fit the functions to experimental data so as to find the 4 parameters that minimize both the objectives? Are there any solvers in the 'Multiobjective Optimization' that can help me with this problem?