How to write a summation with index vector in the objective function?

Hi, I want to do this optimization problem in Matlab,

I don't know how to do this summation with i belongs to varLambda_0, I write the code for varLambda_0, but I think it might be useless. BTW, we cannot drop the unnecessary elements in z, because we still need to use z to do the same optimization problem in the next stage. like

Thanks in advance!

for i = 1:length(y2)
    if z(:,i)'*gammahat0_0 > a
        Gamma_0(i)= i; 
    end
end
Gamma_0(Gamma_0==0) = []

Answer 1

[Anmol Dhiman]

I am assuming gamma_hat_0to be vector, Z to be a matrix and Zi be a vector of equal size to gamma_hat_0. I am assuming a to be constant value

To find the lambda_0 from the first equation use

lambda_0=[];
for i =1: size(z,2)
    temp = (z(:,i)'.*gamma_hat_0);
    % temp will be a vector. Checking if every value in temp is greater
    % than a
    check = temp>a;
  
    if(~ismember(0,check))
        lambda_0(end+1)=i;
    end
end

Each value of lambda_0 in the second equation can be used as

for i=1:length(lambda_0)
    current_value = lambda_0(i);