Identify the coefficients of each constraint separately

I have 4 restrictions below. I would like to make an array of coefficients for each constraint separately. I did the first two, I would like to know if it is correct, first, and I would like help to do the remaining two. My ideia is used the linprog function later.

A = [Xk(1) Xk(2) Xk(3) Xk(4) zeros(1,ncolunas)

B= [0 0 0 0 Xk(1) Xk(2) Xk(3) Xk(4)]

[Walter Roberson]

I suggest that you use Problem Based Optimization https://www.mathworks.com/help/optim/problem-based-approach.html

Answer 1

[Walter Roberson]

You want to operate over rows of Y and over colums of Y.

What you do is reshape() Y to be a row vector, and start creating row entries that correspond. For example, if Y is 3 x 5, then one row of coefficients would be like [zeros(1,0), ones(1,3), zeros(1,12)] and another would be [zeros(1,3), ones(1,3), zeros(1,9)], another would be [zeros(1,6), ones(1,3), zeros(1,6)] and so on. You are creating matrices of selectors of which coefficients are to be used in a particular summation.

Once you have the 2D array of selectors, do element-by-element multiplication against reshape(Y,1,[]) -- so each selector 1 in the temporary variable is replaced by the corresponding Yik value. The result becomes your "A" matrix. The b matrix becomes [P(:); L(:)] (at least with respect to the first two variables.)

I need to think a bit more about how to handle the third condition smoothly.

[JOVANI]

Thanks for the reply! Walter, a few days ago I posted a complete question that involves the same constraints I put in this question. I posted it here: https://math.stackexchange.com/questions/4672610/using-linprog-function-for-a-linear-program. Based on this question, do you think the same reasoning as your answer applies?

[Walter Roberson]

I recommend that you use Problem Based Optimization to construct the constraint matrices. It should also be able to figure out that linprog() can be used as the solver.