I have no idea how the author of this thesis has applied the condition in the title, taken by the Pachamanova’s Lemma (see pag. 29, *Theorem 3.4.1*), to construct the inequality matrix (4.2) at page 34.

Indeed this inequality will be necessary to pass from the robust counterpart (4.14) to the matrix inequality in (4.15) (see pages 36-37).

What I know is that Pachamanova, in her Theorem, supposes to define an uncertainty set for $widetilde{A}$ such that $U=begin{Bmatrix}

widetilde{A}|underline{A}leq widetilde{A}leq overline{A}

end{Bmatrix}Rightarrow P^A=begin{Bmatrix}

vec(widetilde{A})|Gcdot vec(widetilde{A})leq d

end{Bmatrix}$.

So, as far as I understood, the author of this thesis consider the problem (4.14) like a dual that can be transformed (for the two-sided relationship between primal and dual problem) in a primal with constraints $Gcdot vec(widetilde{A})leq d$ but I don’t understand how to apply **practically** this formula in the passage (4.14)$rightarrow$(4.15). For example, I really don’t understand how to construct the matrix $G$. Pachamanova says, I quote, in the Theorem 3.4.1 that *“$widehat{x}_iin mathbb{R}^{(m times n)times1}$ contains $widehat{x}$ in entries $(i-1)cdot n+1$ through $i times n$ and $0$ everywhere else”* (see also here, page 26). Well, what does it means? And how should I use this fact to construct my matrix $G$ as well in (4.2) as in (4.15)?

In the end, I’ve understood the concept in theory but I can’t put it into practice. Could you please explain me, or even show me, the passages to construct the (4.15)? I’m really stuck.

Thanks in advance for any help!