Constraint Optimization: argmin dot product between two vectors

I'm trying to solve this optimization problem

Find vector y given two constraints (box constraint and equality constraint over y) and a vector x that minimize the scalar product between them.

Is there a MATLAB function that performes this optimization? I read about fmincon(fun,y,[],[],Aeq,beq,lb,ub) but i don't understand if and how i can set scalar product in fun parameter and if it solves my problem.

Thank you very much in advance!

EDIT: x is known

[Walter Roberson]

I am not clear as to whether x is known, or if x and y both need to be found?

[ickarus]

I'm sorry, i did not specify. Yes x is known!

Thank for your interest!

[Murali Krishna AG]

Hi, I need help on this.

u=argmin{||X-A*w-B*v||^2} with no constraints

Inputs : A,B,X,w,v matrices

outputs:u which contain optimized vector of w,v.

I knew that i have to use fminunc ,how to write code using this.Please help me

[Walter Roberson]

Inputs : A,B,X,w,v matrices

But those are all the variables involved in the equations, so there are no parameters to be found ??

outputs:u which contain optimized vector of w,v.

?? I think you are going to need to explain more clearly.

You should open your own Question on this matter.

Answer 1

[Walter Roberson]

In the below, the A is exactly the same as in your Ay=b constraint, and the b is exactly the same as in that constraint. Typically A and b are used for linear inequality constraints rather than linear equality.

x = .... as appropriate
A = .... as appropriate, your linear equality matrix
b = .... as appropriate, your rhs of your linear equality
Aineq = []; bineq = [];  %linear inequalities are not being used here
lb = zeros(size(x)); ub = v .* ones(size(x));  0 <= y <= v
[y, fval] = fmincon(@(y) dot(x,y), Aineq, bineq, A, b, lb, ub);

[ickarus]

Thanks you a lot for your answer! I have a little question...

Why you set upper bound as ub=v.*ones(size(x)) and not ub=v ?

Thank you very much!

[Walter Roberson]

v is potentially a scalar. If you set an upper bound to a scalar, then instead of copying that scalar for the locations not specifically set, MATLAB would use +inf for the bound for those locations. Using v .* ones(size(x)) creates an array of 1's the same size as x and multiplies it by v, which gives you an array result. It makes the difference between (say) [7 inf inf] and 7*[1 1 1] = [7 7 7]