Dear all,

I am sorry to bother you. Recently, I have been learning convex optimization and The DCP Rulerset. I clearly understand that I must prove the function is convex before using CVX. That’s difficult.

As we all know, p-norm is convex when p\geq 1 and that is easy to prove according to the properties of the norm.

But I have an optimization problem shown as follows:

where w is a constant vector, m_1,c_1(i),k_1(i),m_2 are constants, c_2,k_2 are scalars.

I just cannot understand **a function’s infinity norm** means in mathematics. I tried to find some helpful information but failed. So I want to know how to learn the **a function’s infinity norm** and prove it is convex or not.

Thank you very much in advance.

The Markdown code cannot display all the equations, so I paste the picture.