finding a vector that minimises a a sum of series

Hi! I'm new and do not have a lot of knowledge regardering Matlab.

I would like to find a vector that minimises function , where A is matrix and is given; A = [1 2 3 2; 1 0 2 0; 2 3 0.5 4].

Thanks for your answer! :)

Eva

[David Goodmanson]

Hi Eva,

are there any other conditions on x, such as its norm = 1? Otherwise, any x with small values will minimize that function.

[Eva12345]

Hi @David Goodmanson!

Sorry, of course there is another condition, that is that the sum of vector's components is 1; and that for all i.

[Matt J]

The sum you have written is over the first 3 columns of A. Why is the 4th column of A unused?

[Eva12345]

Hi @Matt J,

The 4th column of A is unused because I gave a matrix A just for example, so I would like to solve this optimization problem in general, the only important thing is that matrix A has 3 or more columns.

Do you maybe know how to write code for the problem described above? I would really appreciate your answer.

Eva

Answer 1

[Preyas Sharma]

Hi Eva,

As per my understanding you need to find a vector x that can minimise your given function. In order to achieve it. you can use fmincon function

A = [1 2 3 2; 1 0 2 0; 2 3 0.5 4];
lb = [0,0,0];
ub = [1,1,1];
x0 = (lb + ub)/2;
Aeq = [1 1 1];
beq = [1];
fun = @(x)(max([x(1) x(2) x(3)]*A(:,1:3)));
[x,y] = fmincon(fun,x0,[],[],Aeq,beq,lb,ub);

Expected output:

x =

0.0489 0.5315 0.4196

y =

1.4196

here the constraint is satisfied and the function is minimised.

Hope that resolves your doubt.