Practical Robust Optimization - an introduction - - LNMB

RC for ball uncertaintyThis is equivalent to:(a+Bζ) T x ≤ β ∀ζ : ‖ζ‖ 2 ≤ 1. (2)a T x+ max (B T x) T ζ ≤ β,ζ:‖ζ‖ 2 ≤1Intermezzo: max ζ {d T ζ : ‖ζ‖ 2 ≤ 1} ormax{d T ζ : ζ T ζ ≤ 1}Lagrange: d = λζ, andλ = ‖d‖ 2 .Optimal objective value: dT dλ = ‖d‖ 2.Hence (2) is equivalent to:a T x+‖B T x‖ 2 ≤ β.F A C U L T Y O F E C O N O M I C S A N D B U S I N E S S A D M I N I S T R A T I O N26 / 53