Simple Optimization with integer vector

Dear all,

I have a very easy optimization problem but I am not sure how do formulate it for the optimization toolbox.

The basic version of my problem is the following: f= max A*B

in which B is vector of decision variables: B = [b(1); b(2); ...; b(n)]

and A is a vector (length: n) filled with integers (real world data): e.g. A = [53; 12; ...; 47]

then I have a matrix C with simple constraints regarding the range of b(i). So I want to find the the n optimal values of b(i) (constrained by C).

My assumption was, that I could just use intlinprog for this:

x = intlinprog(f,A,B,C) ... but it doesn't work like that.

Do you guys have an idea how to formulate this for intlinprog (or which command to use instead)

Thanks a lot!

[Torsten]

Do you mean you want to maximize

transpose(A)*B ?

Best wishes

Torsten.

[fr_sk]

Hello Torsten, thanks for the response. I want to maximize

A .* B

where A contains real-world data and B contains variables that can take on the values constrained by C.

[John D'Errico]

Whatare your constraints?

Bound constraints?

LINEAR equality constraints?

LINEAR inequality constraints?

What is C? What does it mean? You cannot simply state that B is constrained by C. That has no meaning, to anyone but you.

Next, You state you want to maximize A.*B. Again, thismakes no sense, since A.*B wll generate a VECTOR. You cannot optimize a vector.

So do you want to maximimze A*B, i.e, dot(A,B)?

Answer 1

[John D'Errico]

First, read the help for intlinprog.

Next, intlinprog is a minimizer. You want to maximize. Assuming that you really need to maximize dot(A,B), where A is a vector, then you would need to minimize dot(-A,B) using intlinprog.

Once you are able to tell me what the constraints are in C, I will answer the remainder of your question.

[fr_sk]

Hello John D'Errico,

thanks for your answer, I am going to try to specify my problem:

Let's say I want to optimize the following functions

2x(1) + 5y(1)

6x(2) + 7y(2)

4x(3) + 3y(3)

... ...

x(n) + y(n)

constrained by

x(1,2,...n) >= 20

y(1,2,...n) >= 10

x(1,2,...n) > 0

y(1,2,...n) > 0

The integers for these problems are stored in vectors of length n:

A = [2; 6; 4; ...]

B = [5; 7; 3; ...]

I now want to obtain the optimal (let's say it's an minimization) n values for x(1,2,...,n) and y(1,2,...,n).

Thanks a lot for looking into this.