I have a target dependent variable "efficiency" ,$F$, and its output (from 0 to 1) can be affected by three parameters: $F(\gamma, \epsilon, \alpha)$. The baseline case values for these parameters are: $$\gamma=0.0073, \epsilon=0.3, \alpha=0.02$$
I have identified the equation for each parameter: $$F(\gamma, 0.3, 0.02)=-972176(\gamma)^4+55948(\gamma)^3-1212(\gamma)^2+12.2(\gamma)+0.71$$ $$F(0.0073,\epsilon, 0.02)=7.76(\epsilon)^4-17.62(\epsilon)^3+11.34(\epsilon)^2-2.77(\epsilon)+0.97$$ $$F(0.0073, 0.3, \alpha)=-11535(\alpha)^4+1061(\alpha)^3-39.5(\alpha)^2+0.0055(\alpha)+0.76$$
All functions are 4th-degree polynomials. The purpose here is to maximize efficiency $(F)$ while varying the three independent variables at the same time, so we can find the right values for $\gamma, \epsilon, \alpha$ that maximize efficiency $(F)$.
I would like to do this on Matlab, but I don't even know what kind of optimization is this. Multi objective is not, because there is only one target function. Multivariable is not either, because the three equations are single-variable each. So I do not know how to look in Matlab docs.
Please help