# Optimization of multivariate non-linear function with linear constraint

I have this huge and ugly function. $$f\left(x,y\right)=$$
$$\frac{\left(1-C^xW^y\right)*{(1-C)}^{\left(1-C\right)x}*{\left(1-W\right)}^{\left(1-W\right)y}*C^{Cx}*W^{Wy}}{\left[{\left(1-C\right)}^{\left(1-C\right)x}*{\left(1-W\right)}^{\left(1-W\right)y}*C^{Cx}*W^{Wy}\right]+{[(1-C)}^{Cx}*C^{\left(1-C\right)x}*W^y]+{[C^x*(1-W)}^{Wy}]}$$ Subject to this constraint: $$Ax+By <= D$$.
$C, W, A, B$ and $D$ are constants, and variables are $x$ and $y$.
This is only a simplified version of the real function. The real function contains more than two variables (so probably I won't be able to use variable substitution).
Is there any known method to solve (or estimate) this optimization problem (Multivariate nonlinear goal function with linear constraint)?

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