Stochastic Programming - Index of

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DYNAMIC SYSTEMS 157 and Practice <strong>of</strong> Decision Analysis. Cambridge University Press, Cambridge, UK. [9] Wets R. J.-B. (1989) The aggregation principle in scenario analysis and stochastic optimization. In Wallace S. W. (ed) Algorithms and Model Formulations in Mathematical <strong>Programming</strong>, pages 91–113. Springer- Verlag, Berlin.
158 STOCHASTIC PROGRAMMING
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Stochastic Programming Second Editi
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Contents Preface . . . . . . . . .
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CONTENTS v 3.6 Simple Recourse . .
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Preface Over the last few years, bo
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PREFACE ix more explicitly with the
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1 Basic Concepts 1.1 Motivation By
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BASIC CONCEPTS 3 solutions. These a
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BASIC CONCEPTS 5 will be lost. In s
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BASIC CONCEPTS 7 1.2 Preliminaries
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BASIC CONCEPTS 9 with center ˆx an
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BASIC CONCEPTS 11 Figure 2 Determin
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BASIC CONCEPTS 13 (except for U). S
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BASIC CONCEPTS 15 may be wait-and-s
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BASIC CONCEPTS 17 dual decompositio
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BASIC CONCEPTS 19 and an empirical
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BASIC CONCEPTS 21 1.4 Stochastic Pr
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BASIC CONCEPTS 23 Figure 8 Measure
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BASIC CONCEPTS 25 These properties
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BASIC CONCEPTS 27 Figure 10 Classif
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BASIC CONCEPTS 29 Figure 12 Integra
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BASIC CONCEPTS 31 µ(A) =0alsoP (A)
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BASIC CONCEPTS 33 Hence, taking int
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BASIC CONCEPTS 35 Consequently, for
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BASIC CONCEPTS 37 Proof For ˆx, ¯
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BASIC CONCEPTS 39 Figure 13 Linear
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BASIC CONCEPTS 41 Figure 15 Differe
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BASIC CONCEPTS 43 However—for fin
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BASIC CONCEPTS 45 Figure 17 Induced
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BASIC CONCEPTS 47 Hence the feasibl
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BASIC CONCEPTS 49 Figure 19 λ = 1
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BASIC CONCEPTS 51 and hence P (λS
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BASIC CONCEPTS 53 The sequence of s
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BASIC CONCEPTS 55 is satisfied. Giv
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BASIC CONCEPTS 57 Now either z is a
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BASIC CONCEPTS 59 Figure 22 Polyhed
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BASIC CONCEPTS 61 Figure 23 Polyhed
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BASIC CONCEPTS 63 Figure 25 LP: unb
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BASIC CONCEPTS 65 this case, the re
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BASIC CONCEPTS 67 Step 3 Exchange t
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BASIC CONCEPTS 69 bases for any lin
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BASIC CONCEPTS 71 ✷ Example 1.6 C
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BASIC CONCEPTS 73 which, observing
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BASIC CONCEPTS 75 is equal to the p
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BASIC CONCEPTS 77 solve the program
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BASIC CONCEPTS 79 {v | Wv =0,q T v0
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BASIC CONCEPTS 81 The feasible set
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BASIC CONCEPTS 83 1.8.1 The Kuhn-Tu
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BASIC CONCEPTS 85 Figure 28 Kuhn-Tu
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BASIC CONCEPTS 87 Figure 29 The Sla
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BASIC CONCEPTS 89 and observing tha
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BASIC CONCEPTS 91 where the bounded
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BASIC CONCEPTS 93 λŷ +(1− λ)ˆ
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BASIC CONCEPTS 95 “reasonable”
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BASIC CONCEPTS 97 1.8.2.3 Penalty m
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BASIC CONCEPTS 99 To simplify the d
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BASIC CONCEPTS 101 Now let us come
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BASIC CONCEPTS 103 Wait-and-see pro
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Page 117 and 118: BASIC CONCEPTS 107 Optimization: No
Page 119 and 120: 2 Dynamic Systems 2.1 The Bellman P
Page 121 and 122: 112 STOCHASTIC PROGRAMMING purpose
Page 123 and 124: 114 STOCHASTIC PROGRAMMING In this
Page 125 and 126: 116 STOCHASTIC PROGRAMMING Proof Th
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Page 129 and 130: 120 STOCHASTIC PROGRAMMING Stage 0
Page 133 and 134: 124 STOCHASTIC PROGRAMMING Table 1
Page 137 and 138: 128 STOCHASTIC PROGRAMMING situatio
Page 139 and 140: 130 STOCHASTIC PROGRAMMING 2.5 Stoc
Page 141 and 142: 132 STOCHASTIC PROGRAMMING Using th
Page 143 and 144: 134 STOCHASTIC PROGRAMMING 2.6 Scen
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Page 147 and 148: 138 STOCHASTIC PROGRAMMING procedur
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Page 153 and 154: 144 STOCHASTIC PROGRAMMING • A tw
Page 155 and 156: 146 STOCHASTIC PROGRAMMING Figu
Page 157 and 158: 148 STOCHASTIC PROGRAMMING 2.8.1 A
Page 159 and 160: 150 STOCHASTIC PROGRAMMING 2.8.2 Fu
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Page 171 and 172: 162 STOCHASTIC PROGRAMMING Hξ pos
Page 173 and 174: 164 STOCHASTIC PROGRAMMING pos W po
Page 175 and 176: 166 STOCHASTIC PROGRAMMING Figure
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Page 183 and 184: 174 STOCHASTIC PROGRAMMING • If t
Page 185 and 186: 176 STOCHASTIC PROGRAMMING Figure 1
Page 187 and 188: 178 STOCHASTIC PROGRAMMING is diffi
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Page 191 and 192: 182 STOCHASTIC PROGRAMMING Edmundso
Page 193 and 194: 184 STOCHASTIC PROGRAMMING Edmundso
Page 195 and 196: 186 STOCHASTIC PROGRAMMING The goal
Page 197 and 198: 188 STOCHASTIC PROGRAMMING which eq
Page 199 and 200: 190 STOCHASTIC PROGRAMMING random v
Page 201 and 202: 192 STOCHASTIC PROGRAMMING increase
Page 203 and 204: 194 STOCHASTIC PROGRAMMING φ β α
Page 205 and 206: 196 STOCHASTIC PROGRAMMING change i
Page 207 and 208: 198 STOCHASTIC PROGRAMMING Figure 2
Page 209 and 210: 200 STOCHASTIC PROGRAMMING The mini
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Page 215 and 216: 206 STOCHASTIC PROGRAMMING Hence, w
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208 STOCHASTIC PROGRAMMING Figure 2
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210 STOCHASTIC PROGRAMMING since th
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212 STOCHASTIC PROGRAMMING or later
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214 STOCHASTIC PROGRAMMING problem
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216 STOCHASTIC PROGRAMMING procedur
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218 STOCHASTIC PROGRAMMING where
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220 STOCHASTIC PROGRAMMING Remember
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222 STOCHASTIC PROGRAMMING φ ( ) F
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226 STOCHASTIC PROGRAMMING By assum
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230 STOCHASTIC PROGRAMMING work, wh
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232 STOCHASTIC PROGRAMMING problem.
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234 STOCHASTIC PROGRAMMING Madansky
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236 STOCHASTIC PROGRAMMING 5. Show
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238 STOCHASTIC PROGRAMMING [16] Dup
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240 STOCHASTIC PROGRAMMING J.-B. (e
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244 STOCHASTIC PROGRAMMING Proposit
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246 STOCHASTIC PROGRAMMING (f T ,g
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248 STOCHASTIC PROGRAMMING covarian
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250 STOCHASTIC PROGRAMMING With the
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252 STOCHASTIC PROGRAMMING It is st
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254 STOCHASTIC PROGRAMMING Hence we
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256 STOCHASTIC PROGRAMMING Taking t
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258 STOCHASTIC PROGRAMMING reader m
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264 STOCHASTIC PROGRAMMING that is,
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266 STOCHASTIC PROGRAMMING pos W po
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272 STOCHASTIC PROGRAMMING min{2x r
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274 STOCHASTIC PROGRAMMING directio
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276 STOCHASTIC PROGRAMMING [5] Gree
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278 STOCHASTIC PROGRAMMING outlined
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280 STOCHASTIC PROGRAMMING since we
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282 STOCHASTIC PROGRAMMING 2 1 a b
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286 STOCHASTIC PROGRAMMING 6.2.1 Th
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288 STOCHASTIC PROGRAMMING a soluti
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290 STOCHASTIC PROGRAMMING Since th
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292 STOCHASTIC PROGRAMMING It is no
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294 STOCHASTIC PROGRAMMING [-1,1] [
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296 STOCHASTIC PROGRAMMING for some
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298 STOCHASTIC PROGRAMMING +/- 1 1
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300 STOCHASTIC PROGRAMMING 1 (-1,0)
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302 STOCHASTIC PROGRAMMING with a g
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304 STOCHASTIC PROGRAMMING First, i
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306 STOCHASTIC PROGRAMMING Table 1
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310 STOCHASTIC PROGRAMMING Universi
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314 STOCHASTIC PROGRAMMING duality
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316 STOCHASTIC PROGRAMMING best-so-
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