Stability and Robustness: Reliability in the World of Uncertainty

OutlineThe World of UncertaintyRobust OptimizationStability AnalysisConclusionMeasuring deviation from the optimumRelative ErrorFor t 0 ∈ P m (C 0 ) and C ∈ R m×n+ , we introduced a so-called relativeerror of t 0 :ε P (C, t 0 ) = maxt∈TTransformation in scalar casemin f i (C, t 0 ) − f i (C, t).i∈N m f i (C, t)In the scalar case, i.e. for m=1, the Pareto set transforms into the setof optimal solutions. Therefore the relative error ε P (C, t 0 ) convertsinto:f 1 (C, t 0 ) − min f 1(C, t)t∈Tε P (C, t 0 ) =min f 1(C, t)t∈T.Yury NikulinStability and Robustness: Reliability in the World of Uncertainty