Electronic Companion – “Solving Two-stage Robust Optimization Problems

MP1 : min y,η cy + η s.t. Ay ≥ d η ≥ (h−Ey −Mul ) π∗ l , ∀l ≤ k y ∈ Sy, η ∈ R. Derive an optimal solution (y∗ k+1, η ∗ k+1) and update LB = c Ty∗ k+1 + η ∗ k+1. 3. Call the oracle to solve SP1 in (2) in Section 2, i.e. Q(y∗ k+1), and derive an optimal solution (uk+1, π ∗ k+1). Update UB = min{UB, cTy∗ k+1 +Q(y∗ k+1)}. 4. If UB − LB ≤ 2, return y∗ k+1 and terminate. Otherwise, update k = k + 1 and go to Step 2 with addition of the following constraint to MP1. η ≥ (h−Ey −Muk+1) π∗ k+1