I would really appreciate it if anyone can help me with my question.
I'm dealing with a multi-objective optimization problem which I simplified here with just two variables to get some insight. Let's consider that we have two functions $f_1(x_1,x_2)=\frac{ax_1}{bx_2+c}$ and $f_2(x_1,x_2)=\frac{dx_2}{ex_1+f}$. The goal is to maximize $f_1(x_1,x_2)$ and $f_2(x_1,x_2)$ over $0\leq x_1\leq 1$ and $0\leq x_2\leq 1$. By deriving the Hessian matrix I know that $f_1$ and $f_2$ are jointly concave with respect to $x_1$ and $x_2$. I am looking for a proper tools for solving this problem in matlab. Can anyone guide me?
Thank you in advance!