Need some help understanding how to vectorise constraint definition.

[Arjun-Mohan]

I'm using CVXR for the first time today, to perform a minimization of a max of a set of variables.

So i set my objective function as:

    O_j <- Variable(20)
    objective <- Minimize(max_entries(O_j))

So this should minimise the maximum of the 20 O_j values, as I understand it from the CVXR documentation.

Now in defining constraints, I am having issues in defining sets of constraints. Since I have 20 variables (and 2 more sets of 20 variables, which are mu_j and sigma_j), defining 20 constraints line by line is obviously tedious, and I am sure there is some way of aggregating this, for constraints that work by the universal quantifier/for all.

for example, one constraint is:

O[j] = 1-pnorm((C([j] -mu[j])/sigma[j])
for all j=1,2,3....20 (C is a constant vector of length 20)

I can replace the generic pnorm in R with p_norm in CVXR. But how will I aggregate all 20 constraints in one line of code? I'm new to using this package so I'm a bit confused.

Additionally, can functions like sqrt be used in constraints the same way or is there an equivalent for CVXR? I have a constraint which is:

`sigma[j] = sqrt(sum(P[i] * (1 - P[i]) * X[i,j] ) `

for all j = 1,2,3....20. Here, P is a constant vector of length 30. X is a variable defined as:

X_ij<-Int(30,20)
Now the sum here works like the excel function SUMPRODUCT(), that is,

P[1] * (1-P[1]) * X[1,j] + P[2] * (1-P[2]) * X[2,j] + ... + P[30] * (1-P[30]) * X[30,j]

I would normally do this using dplyr if I knew the values of X[ i , j ]. Will sum_entries work here?

The code works fine if I define each constraint line by line, but there must be a more efficient way to do this right? I know these doubts are pretty basic but I'm just starting to learn how to code with R/CVXR and any help would be appreciated. Thanks.

[Arjun-Mohan]

This isn't a bug or anything, but I am unable to find any other location to ask doubts about the understanding of the code.

[bnaras]

I am afraid your question is not at all clear. You state:

 O_j <- Variable(20)

and further down, you state

O[j] = 1-pnorm((C([j] -mu[j])/sigma[j])

for all j=1,2,3....20 (C is a constant vector of length 20)

Assuming mu and sigma are constant vectors, what is O ( as opposed to O_j) and how does it relate to the problem? (It surely cannot be the same as O_j, because then you have forced your solution with the equality. Incidentally, use == for equality constraints.)

To avoid having to code a constraint for every index, think matrices. For example, the quick intro on https://cvxr.rbind.io provides one such.

[Arjun-Mohan]

I apologise, it was late at night and my doubt wasnt clear.

This is my problem formulation, basically. mu and sigma are not constants, they are also to be calculated.

I defined my variables as:

O_j <- Variable(20)
mu_j <- Variable(20)
sigma_j <- Variable(20)
x_ij <- Int(30,20)

So now as you can see from the image, those constraints are defined for all j's.

In the line I incorrectly wrote above, I was basically writing how I would define it in regular R coding, that's why I used pnorm() and not p_norm. A single constraint would be:

const1<-1-p_norm((C[1]-mu_j[1])/sigma_j[1])

I could repeat this 20 times, obviously. But how would I do this in a single line? Can I just use the entire matrix, such as:

const1<-1-p_norm((C-mu_j)/sigma_j)

C, and P_i (the values from the image) are two vectors which have precalculated constant values.

So how would I vectorise the constraint definition, if the way I mentioned above wont work?

Finally, do I use the sqrt(), or is there a CVXR equivalent like how p_norm() is for pnorm()

[Arjun-Mohan]

i tried using the quick intro as reference, but there i get a second issue which is, can I use matrices in p_norm as well? will it index each element of the matrix as desired?

similarly, when I am doing the 4th constraint, I want it to take the row sum of x_ij across [i] and set that equal to N[i] (which is a constant). If I use sum_entries here will it sum just the rows?