# Least Squares Minimization of operator norm
**URL:** https://discourse.julialang.org/t/least-squares-minimization-of-operator-norm/53723
**Category:** Optimization (Mathematical)
**Created:** [January 21, 2021, 1:29pm UTC](https://discourse.julialang.org/t/least-squares-minimization-of-operator-norm/53723 "2021-01-21T13:29:57Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@cheng\_chen](https://discourse.julialang.org/u/cheng_chen)
#### Post date: [January 21, 2021, 1:29pm UTC](https://discourse.julialang.org/t/least-squares-minimization-of-operator-norm/53723/1 "2021-01-21T13:29:57Z")
Here is a minimal example of my problem: I want to find a minimizer x that minimizes the objective function :
```julia
opnorm(A*x-b,2)^2
```
I tried Convex.jl, but it doesn’t work for the operator norm.
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### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [January 21, 2021, 1:33pm UTC](https://discourse.julialang.org/t/least-squares-minimization-of-operator-norm/53723/2 "2021-01-21T13:33:29Z")
> [@cheng\_chen](#):
>
> `opnorm(A*x-b,2)^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?
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### Author:  [@cheng\_chen](https://discourse.julialang.org/u/cheng_chen)
#### Post date: [January 21, 2021, 3:12pm UTC](https://discourse.julialang.org/t/least-squares-minimization-of-operator-norm/53723/3 "2021-01-21T15:12:39Z")
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.
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### Author:  [@ericphanson](https://discourse.julialang.org/u/ericphanson)
#### Post date: [January 21, 2021, 3:24pm UTC](https://discourse.julialang.org/t/least-squares-minimization-of-operator-norm/53723/4 "2021-01-21T15:24:56Z")
`opnorm` is for operators (matrices), which I think is what @stevengj is getting at here. Do you mean `norm` instead?