Problems with the pow_p and a convex input x - need help for alternative representation

Nonconvex
Oct 10, 2016
R

Dear all,

I have a problem in my CVX program, where a convex function:

\eta(x) = a*x*(1+(\frac{x}{b})^4)

is at the left hand side of my constraint. a and b are given constants

The problem is that my x is a norm of a matrix, so convex, and CVX does not accept any of the power functions in order to represent the 4th power of x. I get the following error message:
Disciplined convex programming error:
Illegal operation: pow_p( {concave}, {4} )

Can anyone suggest a proper reformulation?

Thank you in advance. :slight_smile:

M

The fact that the error says the input to pow_p is concave suggests that it is not the norm of a matrix as you claim it to be.

Regardless, as the help documentation for pow_p states, it can accept only affine inputs. You will have more luck with pow_pos, which is the monotonic extension of pow. Still, that requires a convex input.

M

But even if you get past that problem, you have another product in your expression that will be forbidden. Your problem is very likely not convex. Please read the FAQ.

R
Replying to #3

Yes, I was worried about the product too. Ok, anyway thank you for the immediate reply.