What is Robust portfolio optimisation, uncertainty set?

Robust portfolio optimisation maximises the worst case of the objective over an uncertainty set of inputs. For an ellipsoid of alphas $\{\alpha + \Omega^{1/2}u : \lVert u\rVert \le \kappa\}$ the worst-case expected return is $\alpha^\top w - \kappa\sqrt{w^\top\Omega w}$, and the problem is a second-order cone programme (Goldfarb and Iyengar).