\overline{\upsilon}_o\\
\end{aligned}\end{aligned}$$ [*Proof*]{}: Appendix \[p-suboptlem\].

The differences between and are as follows:

-   The solution to is obtained by the parameter vector optimization individually at each orientation, while the solution to is a parameter vector optimal for all orientations.

-   The optimization problem does not require the computation of $\mathcal{M}$ at each iteration of optimization. To solve , the cost function $\mathcal{M}$ is computed at each iteration of optimization.

The differences between and are as follows:

-   The norm in can be of any type, but in , it has to be consistent and satisfies the sub-multiplicative property.

-   In , $\mathcal{M}=M+m$, but $\mathcal{M}$ can be any combinations of $M$ and $m$ in .

Norm Selection
--------------

Any norm type can be used in and . However, if $\mu_i \neq 0$ and $\mu_i \neq 1$, $i=1,2$, only can be applied, not . The prerequisite to apply is that the sub-multiplicative property must hold for the norm.

There are also some other features associated with the norm definitions that might be important. If 1- or $\infty$-norms of the matrix is chosen, because they are associated with the maximum absolute column and row of the matrix, certain features, which are not along 