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| Kuhn D. — Generalized Bounds For Convex Multistage Stochastic Programs |
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| Предметный указатель |
 -Algebra of events 7
Adjusted recourse problem 88 95 101
Anticipative policy see “Policy”
Attouch 81
Augmented probability space 30
Auxiliary recourse problem 73
Auxiliary stochastic program 73 74
Barycentric approximation scheme 5 53
Barycentric approximation, lower 62
Barycentric approximation, upper 63
Barycentric coordinates 54
Barycentric probability measures 71
Barycentric transition probabilities 71
Barycentric weights 54
Barycentric weights, (generalized) 55
Barycentric weights, (generalized) history-dependent 70
Barycentric weights, history-dependent 69
Biconcave function 40
Biconjugate function 148
Biconvex function 46
Birge 3 6 27 46 65
Border 16
Bounding measure 53
Bounding set 78 111
Bounds on the recourse functions 74—77 88—89 99—100 102 110—111
Branch and bound algorithm 114
Branching factor 53
Capacity constraints 116
Caratheodory map 17
Caroe 115
Closed function 148
Closure of a function 147
Complementary slackness 56
Component coupling constraints 115
Concave conjugate function 148
Concave function 35
Concave function on nonconvex domain 36
Concave function, vector-valued 36
Conditional correction terms for nonconvex constraints 95
Conditional correction terms for nonconvex objective 87
Conditional correction terms for nonconvex objective and constraints 101
Conditional expectation, regular 9
Conditional expectation, regular w.r.t. barycentric measures 71
Conditional probability, regular 9
Conditional probability, regular w.r.t. barycentric measures 71
Confidence ellipse 117
Conjugate duality 147; see “Duality”
Conjugate function 148
Constraint function 11
Constraint function, defined on the augmented probability space 30
Constraint multifunction 12
Constraint multifunction, non-anticipative 12
Constraint qualification 33
Constraint qualification, Slater 33—34
Convex function 35
Convex function on nonconvex domain 35—188
Convex function, vector-valued 35
Convex hull 148
Correction terms for linear stochastic programs 110
Correction terms for nonconvex constraints 94
Correction terms for nonconvex objective 84
Correction terms for nonconvex objective and constraints 101
Cross-simplex 54
Curse of dimensionality 53
d.c. function 105
Danzig 102
Decision history 10
Decision rule 10
Decision rule, anticipative 10
Decision rule, non-anticipative 10
Deng 120
Dentcheva 115
Dokov 3
Dual problem conjugate duality 150
Dual problem Lagrangian duality with equality constraints 161
Dual problem Lagrangian duality without equality constraints 157
Duality gap 152
Duality, conjugate 147
Duality, Lagrangian 155
Duality, strong 152
Duality, weak 152
Dula 3
Dupacova 3 56
Dynamic constraints 114
Dynamic version 32
Edirisinghe 3 144
Edmundson 3
Edmundson — Madansky inequality 59
Effective profit function 14
Effective profit function, defined on the augmented probability space 31
End effects 127
Energy balance equation 116
Energy conversion factor 118
Epi-convergence 81
Event 7
EVPI see “Expected value of perfect information”
Exact penalty functions 164
Expectation functional 15 32
Expected value of perfect information 7 26
Extended arithmetic 36
Feasible set mapping 12 32
Feasible set mapping, nested 12 32
Filtration 7
Filtration, induced 8
Fleten 115
Frauendorrnr 3 5 29 53 54 66
Fubini's theorem (generalized) 20
Gassmann 3
Generalized barycenters 61 63
Generalized barycenters, history-dependent 70
Generalized barycentric weights see “Barycentric weights”
Generalized feasible set 13
Generalized feasible set, defined on the augmented probability space 32
Generalized Fubini theorem 20
Groewe-Kuska 115
Guessow 115
Hartman 106
Here-and-now 25
Huang 65
Hypograph 147
Induced constraints 12
Induced filtration see “Filtration”
Inverse demand elasticity 119
Inverse demand function 119
| Jensen 2 3
Jensen's inequality 57
Kall 3 65
Klein Haneveld 22
Lagrange multiplier 161
Lagrangian function 150 157 160
Lagrangian relaxation 114
Level set 13
Linear stochastic program see “Stochastic program”
Louveaux 27 46
Madansky 3 26
MILP see “Mixed integer linear program”
Mixed integer linear program 114
Moment problem 53
Morton 3
Multifunction see “Set-valued mapping”
Multistage stochastic program see “Stochastic program”
Natural domain of the expectation functional 15 32
Natural domain of the recourse function 15 32
Nested feasible set mapping see “Feasible set mapping”
Non-anticipative constraint multifunction see “Constraint multifunction”
Non-anticipative policy see “Policy”
Non-anticipativity constraints 114
Normal form of a linear stochastic program 104
Normal integrand 12 19
Normality 152
Objective function coefficients 103
Observation 8
Ostermaier 115
Outcome 7
Outcome history 10 30
Partition of a conditional probability 68
Partition of a probability measure 64
Partition of a set 64
Penalty formulation 163—164
Pereira 114
Pflug 4 78
Pinto 114
Policy 10
Policy, anticipative 10
Policy, non-anticipative 10
Primal problem conjugate duality 150
Primal problem Lagrangian duality with equality constraints 161
Primal problem Lagrangian duality without equality constraints 157
Profit function 14
Profit function, defined on the augmented probability space 30
Proper concave function 147
Proximal bundle method 114
Pseudo-probabilities 60 63
Pseudo-probabilities, history-dependent 70
Rachev 4
Raiffa 26
Random variable 8
Random vector 8
Recourse function 15 32
Recourse matrix 103
refinement 65 71
Refinement parameter 64 68
Regular conditional expectation see “Conditional expectation”
Regular cross-simplex see “Cross-simplex”
Regular refinement strategy 72
Regularity conditions 17 22 24 37 45 46 85 91 100 107
Regularizable constraint function 89
Regularizable profit function 84
Revenue balance equation 125
Rhs vector see “Right hand side vector”
Right hand side vector 103
Risk aversion 123
Rockafellar 12 16 40 47 147
Roemisch 4 114 115
Sample space 7
Scenario generation 1 51
Scenario problem 25
Scenario tree 52
Scenario tree node 52
Scenario tree path probability 52
Schlaifer 26
Schultz 114 115
SDDP see “Stochastic dual dynamic programming”
SDP see “Stochastic dynamic programming”
Set-valued mapping bounded 16
Set-valued mapping continuous 16
Set-valued mapping lower semicontinuous 16
Set-valued mapping upper semicontinuous 16
Shadow price 122
Shapiro 106
Slater point 34
Slater's constraint qualification see “Constraint qualification”
Stability 152
State space 8
Static version 14 31
Stochastic dual dynamic programming 114
Stochastic dynamic programming 113
Stochastic process 8
Stochastic process, adapted 8
Stochastic process, block-diagonal autoregressive 36
Stochastic process, deterministic 8
Stochastic process, nonlinear autoregressive 16
Stochastic process, previsible 8
Stochastic program 1
Stochastic program, convex 29
Stochastic program, dynamic version 14 32
Stochastic program, linear 102
Stochastic program, non-linear 14
Stochastic program, static version 14 31
Strategy 10
Strategy, anticipative 10
Strategy, non-anticipative 10
Subdifferentiability 47—49
Subgradient method 114
Sup-projection 40 169—174
Technology matrix 103
Transition probability 52 68
Truncation 116
Upper semicontinuity 147
Usc hull 147
Utility function 123
Value of the stochastic solution 7 27
VSS see “Value of the stochastic solution”
Wait-and-see 26
Wallace 115
Weak convergence 66
Wets 3 6 12 16 43 65 81 173
Ziemba 3 115
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