CVX: Illegal operation: pow_p( {convex}, {-1} )？

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help pow_p

pow_p Positive branch of the power function.
pow_p(X,P) computes a convex or concave branch of the power function:
P < 0: pow_p(X,P) = X.^P if X > 0, +Inf otherwise
0 <= P < 1: pow_p(X,P) = X.^P if X >= 0, -Inf otherwise
1 <= P : pow_p(X,P) = X.^P if X >= 0, +Inf otherwise
Both P and X must be real.

Disciplined convex programming information:
    The geometry of pow_p(X,P) depends on the precise value of P,
    which must be a real constant:
             P < 0: convex  and nonincreasing; X must be concave.
        0 <= P < 1: concave and nondecreasing; X must be concave.
        1 <= P    : convex  and nonmonotonic;  X must be affine.
    In all cases, X must be real

if the 2nd argument of pow_p is negative, the first argument must be concave (or affine). Hence, the error message.

Unsurprisingly, inv_p also requires its argument to be concave (or affine).

So the first thing you need to do is prove that your model is convex.