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Please, see here at page 3: could you help to understand the proofs from E.1 to E.4? In particular:

  • why, by adding the constraint $\operatorname{c^Tx}-t\leq 0$, did the objective function become certain?

  • What's the meaning of uncertain right-side side of a constraint? I don't understand the rule of $x_{n+1}=-1$.

Then, for E.3 and E.4, total darkness.

Thanks in advance.

Marco Pittella
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1 Answers1

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E.1 is the usual linearization of a min-max problem, replacing the max with an explicit variable $t$ and imposing a constraint on $t$. The uncertainty of $c$ has now moved from the objective to a constraint.

For E.2, suppose you have some constraint $\sum_{j=1}^n a_{i,j} x_j \le d_i$, where $d_i$ is uncertain. You can introduce a new variable $x_{n+1}$ and rewrite the constraint as two constraints: \begin{align} \sum_{j=1}^n a_{i,j} x_j + d_i x_{n+1} &\le 0 \\ x_{n+1} &= -1 \end{align} The uncertainty of $d_i$ has now moved from the right-hand side to the left-hand side (a constraint coefficient).

RobPratt
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