Least Squares Minimization of operator norm

Specific Domains Optimization (Mathematical)
1

Here is a minimal example of my problem: I want to find a minimizer x that minimizes the objective function :

opnorm(A*x-b,2)^2

I tried Convex.jl, but it doesn’t work for the operator norm.

2

If x and b are 1d arrays, this is not defined in Julia. If they are 1-column matrices, this is equivalent to the Euclidean norm. What are the dimensions here?

3

Thank you for your reply!
Let’s say A is d by n, x is n-dimensional and b is d-dimensional, which means A*x-b is d-dimensional.

4

opnorm is for operators (matrices), which I think is what @stevengj is getting at here. Do you mean norm instead?

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