Modelling Frobenius norm of Matrix using one SecondOrderCone() constraint

Specific Domains Optimization (Mathematical)
1

Hi all,

I was wondering if it is possible to model the Frobenius norm of a matrix using a single second order cone constraint in JuMP 0.19 (perhaps by reshaping the matrix).
In JuMP 0.18.5 this was possible via:
@variable(m, X[1:n, 1:m])
@constraint(m, t>=norm(X))

In JuMP 0.19 I can certainly model a Frobenius norm with min(n,m) second order cone constraints, via
@variable(m, t[i=1:n]>=0.0)
@constraint(m, defineSOC[i=1:n], [t[i]; X[i,:]] in SecondOrderCone())
but for performance reasons it would be better to use one SecondOrderCone.

Thanks!

2

Why don’t you do @constraint(model, [t; vec(X)] in SecondOrderCone()) ?

3

Exactly what I was looking for, thanks!

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