Optimization Constraint: One of every two variable pairs must be zero!

Dear Community,

thanks for being so quick with my earlier post. Now, I just ran into another problem:

I apply the fmincon solver to solve an optimization function as follows, with x being of the dimension of [2*8760 x 1]:

fun = @(x) x(:).'*p(:);

Now, I want to constrain that for every two elements of x, one must equal zero. Means, either x1 or x2 is zero; the same for the elements x3 and x4, x5 and x6 and so on...

Doing so, I can only use the constraint syntax as follows:

• a) Aineq*x <= bineq
• b) Aeq*x = beq

So, I would have to define either Aineq or Aeq and bineq or beq to achieve this constraint. One way I thought of:

If I had a function that returns 1 for non-zero elements and zero for zero elements, I could define beq as only zeros and Aeq as:

(func func 0 0 0 0 ...
0 0 func func 0 0 ...
0 0 0 0 func func ...
...)

Which would also lead me to the question: Can I insert functions into constraint matrices? And if yes, how and what would be such a function?

I am really looking forward to your thoughts on this! Thanks a lot!