# How to express this objective and constraints in CVX?

i\in\{1,\dots,N\}
g\in\{1,\dots,N\}

x_{i,g} binary decision variable
y_{i,j,g} binary decision variable

I want to maximize \sum_{i<j}\sum_g w_{i,j} y_{i,j,g}

subject to

\begin{align} y_{i,j,g} &\le x_{i,g} &&\text{for all $i<j$ and all $g$} \\ y_{i,j,g} &\le x_{j,g} &&\text{for all $i<j$ and all $g$} \\ \end{align}

I declare the variable as

           variable X(N,G) binary
variable Y(N,N,G) binary


How can I express the objective and the last two constraints?

Constrains and objectibe should be straightforward using for loops. If you can vectorize at all, CVX formulation will be faster.

The objective can be built up in for loop.

Objective = 0;
for ...
Objective = Objective + ...
end
maximize(Objective)

I am doing this…

  Objective=0;
for g=1:G
for i=1:C-1
for j=i+1:C
Objective=Objective+WeightMatrix(i,j)*Y(i,j,g);
end
end
end


Hopefully I am doing it right…Would you please confirm.

It looks o.k., except that C should be N for consistency with your variable declaration for Y