Practical Robust Optimization - an introduction - - LNMB

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General remarks■■■■■RC reformulations also valid for MIP problems.Structure (e.g. network, total unimodularity) often destroyedby RC.Analyze robustness of nominal and robust optimal solution.There are no methods known that can deal with integeradjustable variables.RO methodology implemented in modelling packages asYalmip, ROME, AIMMS.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 N48 / 53
Extensions■■■■■Tractable robust counterpart for other uncertainty regions,e.g. defined by separable convex functions.Tractable robust counterpart for problems with certain typesof non-affine uncertain parameters.Example: (1+ζ 2 1)x 1 +ζ 1 ζ 2 x 2 ≤ 5, ∀ζ : ‖ζ‖ 2 ≤ 1.Tractable (approximations of) robust counterpart for (conic)quadratic, SDP and other nonlinear problems.Tractable robust counterpart for certain classes of nonlineardecision rules.Globalized robust counterpart for nonlinear optimizationproblems.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 N49 / 53
Page 2 and 3: Overview■Motivation for Robust Op
Page 4 and 5: What sets great optimization apart?
Page 6 and 7: Flaw of using nominal valuesOptimiz
Page 8 and 9: Flaw of using nominal valuesConstra
Page 10 and 11: Flaw of using nominal valuesOptimiz
Page 12 and 13: Flaw of using nominal valuesā T x
Page 14 and 15: Flaw of using nominal valuesAmong 9
Page 16 and 17: Why RO can make a difference ...Ext
Page 18 and 19: BookImportant chapters: Preface, Ch
Page 20 and 21: Relation with Stochastic Programmin
Page 22 and 23: Introduction to robust linear optim
Page 24 and 25: Tractable robust counterparts(a+Bζ
Page 26 and 27: RC for ball uncertaintyThis is equi
Page 28 and 29: Budget uncertainty regionOften used
Page 30 and 31: Planning of Air Traffic Controllers
Page 32 and 33: Planning of Air Traffic Controllers
Page 34 and 35: Safe approximation of chance constr
Page 36 and 37: Bridge that was not robust ...F A C
Page 38 and 39: Multistage problemsSome of the deci
Page 40 and 41: Linear Decision Rule(ARC) (a+Bζ) T
Page 42 and 43: AARC shows often very good behaviou
Page 44 and 45: Advantage of Globalized Robust Coun
Page 46 and 47: Example 2:(RP) |x 1 −ζ|+|x 2 −
Page 50 and 51: Application areas of ROHundreds of
Page 52 and 53: Application: Cancer treatment■ Tr

Practical Robust Optimization - an introduction - - LNMB

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