Practical Robust Optimization - an introduction - - LNMB

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Flaw of using nominal valuesConstraint: a T x = (ā+ρζ) T x = ā T x+ρζ T x ≤ b.Probability of infeasibility= 0.5!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 N8 / 53
Flaw of using nominal valuesOptimization based on nominal values often lead to (severe)infeasibilities.Consider the binding constraints: (a k ) T x ≤ b k ,■a k is uncertain,ā k is nominal value.■ a k = ā k +ρ k ζ k , and−1 ≤ ζ k i ≤ 1.■ζ k are independent and uniformly distributed.k = 1,..,N.Assume: theseN constraints are binding in the optimal solution(fora = ā).Probability of infeasibility= 1− ( 12) N.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 N9 / 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 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 48 and 49: General remarks■■■■■RC re
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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