Presuming \rho_k < 1, use rho_hat*inv_pos(1 - rho_k)
for the RHS of the constraint. I’ll let you fix up the variable names, indexing, etc.
inv_pos Reciprocal of a positive quantity.
inv_pos(X) returns 1./X if X is positive, and +Inf otherwise.
X must be real.
For matrices and N-D arrays, the function is applied to each element.
Disciplined convex programming information:
inv_pos is convex and nonincreasing; therefore, when used in CVX
specifications, its argument must be concave (or affine).
but the meaning of using inv_pos (1-rho_k) and 1/(1-rho_k) are the same.the cvx can just accept inv_pos (1-rho_k) only.
as i said,cvx can’t find the variable value if we put this variable into the denominator,so if we replace 1/(1-rho_k) with inv_pos (1-rho_k) ,the rho_k is still in the denominator.
I know and agree cvx can accept the form you gave,but it can’t optimize and calculate that rho_k value,so replacing 1/(1-rho_k) with inv_pos (1-rho_k) is meaningless for me,there is a constraint that let therho_k <=1 and rho_k >=0,but i did’t show this
I don;t understand why this use of inv_pos is not acceptable to you. You must declare rho_k (or whatever you call it) to be a (CVX) variable. After cvx_end, if the solver finds a solution to your problem,rho_k will have been optimized, and its optimal value will be inserted into rho_k for your use.
After the running of the code,cvx can’t find a value usually,so my teacher told me she remember that if we put a variable into the denominator,the cvx can’t really find the optimal value of that variable.
accept and be calculated the optimal value are two different things,maybe you think they are the same,but they are not in fact.
Again,i agree the cvx can accept the form,inv_pos (1-rho_k),you gave,but it just means the cvx can run your code, it does’t mean cvx can find the rho_k optimal value in this form.
I have no idea what your model is supposed to represent. I have no idea what input data values are meaningful or reflective of some real world situation. This forum is not a forum on creating models for electrical engineering, or whatever this is. For that, you should consult subject matter experts, such as perhaps (hopefully) your teacher. Or if you have taken this from a paper, then consider consulting the authors of the paper.
If your problem is infeasible, then one or more constraints are too stringent. Of course, the problem may be feasible for some values of input data and not for others.
I don’t know what any of that represents, or how the P 's are related to the variables, and what that means for how if at all it can be entered into CVX, nor do I care to put in the time and effort to become knowledgeable in this subject area.