How to constrain a element of variable

MIDCP
1

I defind a variable with dimension 1*n,But i want to constrain the first element and the last element of the variable,to make the two elements larger than maximization of the variable, so how should i do？Is this can achieve?

the code:
cvx_begin quiet
variable wt(Mt-2) complex %variable
minimize(norm(cur_Qt*wt,1));
subject to
At_tar’*wt == 1;
abs(wt(1)) >= max(abs(wt))*0.0001; %%canstrain the first element of the variable
abs(wt(end)) >= max(abs(wt))*0.0001; %%canstrain the first element of the variable
for sl=1:length(sl_ind)
abs(Ats(:,sl)’*wt) <= 10^(desired_psll/20);
end
cvx_end

error:
error using cvxprob/newcnstr (line 192)
Disciplined convex programming error:
Invalid constraint: {convex} >= {real constant}

error >= (line 21)
b = newcnstr( evalin( ‘caller’, ‘cvx_problem’, ‘[]’ ), x, y, ‘>=’ );

2

convex >= constant is a non-convex constraint; therefore, not allowed by CVX. If you want abs(cvx variable) >= constant, you would need to introduce binary variables to handle this non-convex use of the convex function abs. You can search at https://or.stackexchange.com/ and ask for help there on how to do that. You will need to have Gutobi or Mosek available as solver to do this in CVX.

3

Thanks, do you have other simply methods that i can constrain the first element of the varible made it larger than the maxization of the variable?
like: abs(wt(1)) >= max(abs(wt))*0.0001;

4

You are using abs in a non-convex manner, hence the need for binary variables to handle the non-convexity.

5

so i should redefind binary variable or transform variable into binary version,please tell me how to do? I’m not familar with it.

6

AS I wrote, please seek assistance at https://or.stackexchange.com/ .Ask how to convert this to a convex constraint using binary variables.