MATLAB code for Minimization of vectors

Question

Question: What type of optimization function in MatLab should I use to solve the following minimization matrix problem?

I am trying to find the row vector V such that [[ (f – transpose(V) * R) ]] is minimized subject to:

transpose(V)*B = 0.

++++Variables:

• f is a scalar which is known.
• R is (8x1) row vector which is known.
• B is (8x1) row vector which is known.
• V is (8x1) row vector which is unknown and I want to find that.

+++++More Conditions:

• The value of the eight found entries in row vector V (8x1) should be between 0 and 1.

• The sum of the value of all eight entries of row vector V (8x1) should be unity (one).

Thanks, Matt

Answer 1

you should use fmincon:

% random inputs f, R, B
f = rand;
R = 2*rand(8,1) - 1;
B = 2*rand(8,1) - 1;
% minimization term
fun = @(V) abs(f - V'*R);
% constrains: transpose(V)*B = 0 and sum(V) = 1
Aeq = [B';ones(1,8)];
beq = [0;1];
% lower (0) and upper (1) bounds
lb = zeros(8,1);
ub = ones(8,1);
% initial guess
V0 = rand(8,1);V0 = V0/sum(V0);
% constrained minimization
V = fmincon(fun,V0,[],[],Aeq,beq,lb,ub);
% check result
sum(V) % should be 1
V'*B % sould be 0
[min(V) max(V)] % should be between 0 to 1