I have a number of objective functions like:
y1 = a11* x11 + a12*x11*x11+ a13*x12+....... y2 = a21* x21 + a22*x21*x21+ a23*x22+....... ::::: ::::: :::::
These are multiple objective functions. However, the constraints of the objective functions have dependency on each other. Something like,
x11+ x21 + x22 < const1 x12 + x21 > const2 ::::: :::::
What is the way to optimize such a system of equations? I would ideally like to use R to do the same?
y1 = 0.32 x1 + 0.21 x1*x1 + 0.49 x2... y2... y3 . . . The equations that i have is a non-linear function. These are non-linear regression equations or non-linear Market Mix Models. The x's are TV spend, Digital Spend etc. I want to 'include' all these models, use some constraints on them and optimize the spends in all the models with respect to constraints like...x1 (TV spend) < 100, TV + Digital spend < 500. I want to be able to say that of an amount of 100, i should spend, 30 on model 1, 20 on model 2( equation 2) etc