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E-raamat: Systems Optimization Methodology, Pt. 2 [World Scientific e-raamat]

(Chairman Of St Petersburg Univ, Russia)
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Systems Optimization Methodology, Pt. 2Suurem pilt
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World Scientific e-raamatudRohkem infot World Scientific e-raamatute kohta
Raamatu kodulehekülg: http://www.worldscientific.com/worldscibooks/10.1142/3632#t=toc
This monograph deals with theoretical fundamentals and numerical methods of optimizing nondetermined models of systems. The main body of this work is devoted to investigation and optimization of system models under incomplete information. Much consideration is given to one-, two- and multistage problems of stochastic programming, solution methods and problems of solution stability. Optimization problems with fuzzy variables and optimization problems in function spaces are investigated. Examples are given for implementation of specific models of optimization under incomplete information.The book is based on lectures delivered by the author since 1965 for undergraduates and postgraduates at St. Petersburg (Leningrad) State University.
Introduction xi
Risk and Uncertainty in the Complex Systems
1(6)
Uncertainty and probability in the Planning and Management Problems for Complex Systems
1(2)
Probabilistic Approaches to Complex Systems
3(2)
Basic Indications for Classification of Stochastic Programming Problems
5(2)
Chance-Constrained Stochastic Programming Problems
7(30)
Statement and Qualitative Analysis of Chance-Constrained Stochastic Programming Problems
7(5)
Charnes-Cooper Deterministic Equivalents
12(3)
Deterministic Equivalents to Chance-Constrained Stochastic Programming Problems
15(8)
Examples of Chance-Constrained Stochastic Programming Problems
23(14)
Two-stage Stochastic Programming Problems
37(30)
Statement of a Two-stage Stochastic Programming Problem
37(2)
Analysis of a Two-stage Stochastic Programming Problem
39(5)
Some Partial Models of Two-stage Stochastic Programming Problems
44(3)
The Two-stage Nonlinear Stochastic Programming Problem
47(6)
Methods for the Solution of Two-stage Stochastic Programming Problems: Examples
53(8)
Applications of Two-stage Stochastic Programming Problems: examples
61(6)
Multistage Stochastic Programming Problems
67(26)
Formulations of Dynamic Stochastic Programming Problems
67(6)
Qualitative analysis of Multistage Stochastic Problems with a Posteriori Decision Rules
73(3)
A Priori Decision Rules in Multistage Stochastic Programming Problems
76(8)
Duality in Multistage Stochastic Programming
84(5)
Applications of Multistage Stochastic Programming Problems
89(4)
Game Approach to Stochastic Programming Problems
93(12)
Game formulation of Stochastic Programming Problems
93(4)
Special cases of the Game G(E+n, F, g)
97(8)
Existence of Solution and its Optimality in Stochastic Programming Problems
105(14)
Dual Stochastic Linear Programming Problems
105(2)
Optimality and Existence of the Solution in Stochastic Programming Problems
107(2)
Investigation of one Stochastic Programming Problem
109(7)
Definition of the Set of feasible Solutions in Hanson's Problem
116(3)
Stability of Solutions in Stochastic Programming Problems
119(24)
Stability of Solutions in Stochastic Linear Programming Problems
119(1)
ε-stability of solutions in the mean
120(5)
Stability of Solutions to Stochastic Nonlinear Programming Problems
125(5)
Feasible Solution and Function Stability with respect to the i-th Constraint
130(4)
Investigation of Absolute Solution Stability
134(5)
Stability in Probability Measure
139(4)
Methods for Solving Infinite and Semi-Infinite Programming Problems
143(44)
Statement of Semi-infinite Programming Problems
144(2)
Duality of Semi-infinite Problems
146(2)
Optimality Conditions for Semi-infinite Programming Problems
148(3)
Existence and Uniqueness of Semi-infinite Programming Problems
151(2)
Methods and Algorithms for Solving Semi-infinite Programming Problems
153(19)
Statement of the Infinite Programming Problem
172(3)
Duality of Infinite Programming Problems
175(4)
Optimality Conditions for Infinite Programming Problems
179(3)
Existence and Uniqueness of a Solution to Infinite Programming Problems
182(1)
Methods and Algorithms for Solving Infinite Programming Problems
183(4)
Optimization on Fuzzy Sets
187(22)
Optimization problems in Large and Complex Systems
187(5)
Optimization of Problems with Nonuniquely Defined Parameters
192(2)
Basic Notions
194(6)
Solution Optimization Algorithms for Linear Programming Problems with Variations in Constraint Coefficients
200(2)
Optimization of Integer LP Problems
202(7)
Optimization of Nonlinear Programming Problems with Nonuniquely Defined Variables
209(20)
Optimization of Problems with Nonuniquely Defined Variables and their Solution Methods
210(4)
Generalization in Nonuniquely Defined Functional Optimization Problems
214(5)
Optimization of Nonlinear Convex Functions with Nonuniquely Defined Coefficients
219(5)
Solution Algorithms for Nonlinear Programming Problems with Nonuniquely Defined Variables
224(5)
Optimization Problems in Function Spaces
229(59)
Topological Spaces
229(8)
Linear Topological Spaces. Fundamentals of Convex Analysis
237(5)
Measure Spaces. Probability Spaces. Modeling of Random Variables
242(5)
Ordered Spaces
247(7)
Linear Optimization in Conditionally Complete Vector Lattices
254(20)
Matrix Games in Conditionally Complete Vector Lattices
274(3)
Optimization Problems on Vector Lattices
277(7)
Generalized Parametric Programming Problem
284(4)
Conclusion 288(1)
Bibliography 289
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