- #1

jkim8512

- 3

- 3

- Homework Statement
- Not a hw

- Relevant Equations
- Minimum or Maximum value of a multivariate function

First thank you for taking your time to take a look at this simple question. And sorry for the informal math language and equations, I hope you guys can understand it.

So, depending on the case, I have 2 or 8 simple quadratic functions f(a), f(b), f(c),… f(z).

Each a,b,c,…,z have a different range for f(a),f(b), f(c), .. ,f(z). These functions are all independent to each other, they are just simple quadratic functions.

These functions adds up to get one value f(T).

The constraint is that the sum of a,b,c,…,z should be a given value N.

And what I want is the Minimum or maximum value of f(T)So, If I right it down in some simple math, it looks like this.

f(T) = f(a) + f(b) + f(c) + f(d)+….+f(z)

constraint: N = a+b+c+d+….+z

goal: Find minimum or maximum value of f(T) when N is given.

where,

f(a) = simple quadratic function such as 3a^2+ 4a+ 5, range: a_start < a < a_end

f(b) = simple quadratic function such as 3b^2+ 4b+ 5, range: b_start < b < b_end

f(c) = simple quadratic function such as 3c^2+ 4c+ 5, , range: c_start < c < c_end

………… same up to f(z)

I googled some stuff and found I could probably use “Max/min for functions of multi variables” things like that.

The main problem I can’t figure out is how to deal with the constraints I need to have regarding N=a+b+c,..+z

Thanks again!

So, depending on the case, I have 2 or 8 simple quadratic functions f(a), f(b), f(c),… f(z).

Each a,b,c,…,z have a different range for f(a),f(b), f(c), .. ,f(z). These functions are all independent to each other, they are just simple quadratic functions.

These functions adds up to get one value f(T).

The constraint is that the sum of a,b,c,…,z should be a given value N.

And what I want is the Minimum or maximum value of f(T)So, If I right it down in some simple math, it looks like this.

f(T) = f(a) + f(b) + f(c) + f(d)+….+f(z)

constraint: N = a+b+c+d+….+z

goal: Find minimum or maximum value of f(T) when N is given.

where,

f(a) = simple quadratic function such as 3a^2+ 4a+ 5, range: a_start < a < a_end

f(b) = simple quadratic function such as 3b^2+ 4b+ 5, range: b_start < b < b_end

f(c) = simple quadratic function such as 3c^2+ 4c+ 5, , range: c_start < c < c_end

………… same up to f(z)

I googled some stuff and found I could probably use “Max/min for functions of multi variables” things like that.

The main problem I can’t figure out is how to deal with the constraints I need to have regarding N=a+b+c,..+z

Thanks again!