I would like to approximate the following equation to be used as an objective function in gurobi Multi-objective optimization.
The continuous decision variables in the above equation are $ I_{i,v}$ and $SOC_{init}$. Everything else is a constant. $SOC_{init}$ can take values between $[0,1]$. From the surface and curve plots below I want to find an approximate equation that is a function of $ I_{i,v}$ and $SOC_{init}$ and has only order/degree of 2. I mean we can have products like $ I_{i,v} \cdot SOC_{init}$ or $ I_{i,v}^2 or \ SOC_{init}^2$ but not beyond that due to gurobi limiation.
The reason I want to find an approximate equation is for gurobi to find solutions quickly (real-time).
This equation yields the following surface:
In 2-Dimension it can be viewed as a set of curves that is a function of $SOC_{init}$
It is ok to only approximate up to $ 0 \leq I_{i,v} \leq 130$ it's not necessary to go all the way to 300.
Calculate values of your function on a $3 \times 3$ Grid, and then use 2D quadratic Lagrange interpolation.