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Bilevel Programming Problems: Theory, Algorithms and Applications to Energy Networks 2015 ed. [Kõva köide]

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  • Formaat: Hardback, 325 pages, kõrgus x laius: 235x155 mm, kaal: 6328 g, 30 Illustrations, black and white; XII, 325 p. 30 illus., 1 Hardback
  • Sari: Energy Systems
  • Ilmumisaeg: 17-Feb-2015
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3662458268
  • ISBN-13: 9783662458266
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Bilevel Programming Problems: Theory, Algorithms and Applications to Energy Networks 2015 ed.Suurem pilt
  • Formaat: Hardback, 325 pages, kõrgus x laius: 235x155 mm, kaal: 6328 g, 30 Illustrations, black and white; XII, 325 p. 30 illus., 1 Hardback
  • Sari: Energy Systems
  • Ilmumisaeg: 17-Feb-2015
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3662458268
  • ISBN-13: 9783662458266
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783662458266.html
Märksõnad:

This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.

1 Introduction
1(20)
1.1 The Bilevel Optimization Problem
1(1)
1.2 Possible Transformations into a One-Level Problem
2(6)
1.3 An Easy Bilevel Optimization Problem: Continuous Knapsack Problem in the Lower Level
8(2)
1.4 Short History of Bilevel Optimization
10(2)
1.5 Applications of Bilevel Optimization
12(9)
1.5.1 Optimal Chemical Equilibria
12(1)
1.5.2 Optimal Traffic Tolls
13(1)
1.5.3 Optimal Operation Control of a Virtual Power Plant
14(1)
1.5.4 Spot Electricity Market with Transmission Losses
15(1)
1.5.5 Discrimination Between Sets
16(2)
1.5.6 Support Vector Machines
18(3)
2 Linear Bilevel Optimization Problem
21(20)
2.1 The Model and First Properties
21(6)
2.2 Optimality Conditions
27(6)
2.3 Solution Algorithms
33(8)
2.3.1 Computation of a Local Optimal Solution
33(2)
2.3.2 A Global Algorithm
35(6)
3 Reduction of Bilevel Programming to a Single Level Problem
41(76)
3.1 Different Approaches
41(6)
3.2 Parametric Optimization Problems
47(5)
3.3 Convex Quadratic Lower Level Problem
52(2)
3.4 Unique Lower Level Optimal Solution
54(8)
3.4.1 Piecewise Continuously Differentiable Functions
55(4)
3.4.2 Necessary and Sufficient Optimality Conditions
59(1)
3.4.3 Solution Algorithm
60(2)
3.5 The Classical KKT Transformation
62(22)
3.5.1 Stationary Solutions
62(7)
3.5.2 Solution Algorithms
69(15)
3.6 The Optimal Value Transformation
84(11)
3.6.1 Necessary Optimality Conditions
85(2)
3.6.2 Solution Algorithms
87(8)
3.7 Primal KKT Transformation
95(5)
3.8 The Optimistic Bilevel Programming Problem
100(17)
3.8.1 One Direct Approach
100(4)
3.8.2 An Approach Using Set-Valued Optimization
104(9)
3.8.3 Optimality Conditions Using Convexificators
113(4)
4 Convex Bilevel Programs
117(16)
4.1 Optimality Conditions for a Simple Convex Bilevel Program
117(8)
4.1.1 A Necessary but Not Sufficient Condition
117(2)
4.1.2 Necessary Tools from Cone-Convex Optimization
119(3)
4.1.3 A Solution Algorithm
122(3)
4.2 A Penalty Function Approach to Solution of a Bilevel Variational Inequality
125(8)
4.2.1 Introduction
125(1)
4.2.2 An Existence Theorem
126(2)
4.2.3 The Penalty Function Method
128(2)
4.2.4 An Example
130(3)
5 Mixed-Integer Bilevel Programming Problems
133(62)
5.1 Location of Integrality Conditions in the Upper or Lower Level Problems
133(3)
5.2 Knapsack Constraints
136(5)
5.3 Weak Solution
141(17)
5.3.1 Regions of Stability
141(2)
5.3.2 Properties of the Solution Sets
143(1)
5.3.3 Extended Solution Sets
144(1)
5.3.4 Solution Functions
145(2)
5.3.5 Weak Solution Functions
147(3)
5.3.6 Optimality Conditions
150(6)
5.3.7 Computation of Optimal Solutions
156(2)
5.4 Optimality Conditions Using a Radial-Directional Derivative
158(16)
5.4.1 A Special Mixed-Discrete Bilevel Problem
158(3)
5.4.2 Some Remarks on the Sets ΨD(x) and R(y)
161(2)
5.4.3 Basic Properties of φ(x)
163(3)
5.4.4 The Radial-Directional Derivative
166(2)
5.4.5 Optimality Criteria Based on the Radial-Directional Derivative
168(5)
5.4.6 Optimality Criteria Using Radial Subdifferential
173(1)
5.5 An Approach Using Monotonicity Conditions of the Optimal Value Function
174(8)
5.5.1 Introduction
174(1)
5.5.2 Problem Formulation
175(1)
5.5.3 Parametric Integer Optimization Problem
175(4)
5.5.4 An Approximation Algorithm
179(3)
5.6 A Heuristic Algorithm to Solve a Mixed-Integer Bilevel Program of Type I
182(13)
5.6.1 Introduction
182(1)
5.6.2 The Mathematical Model
182(1)
5.6.3 The Problem's Geometry
183(4)
5.6.4 An Approximation Algorithm
187(4)
5.6.5 A Numerical Example
191(4)
6 Applications to Natural Gas Cash-Out Problem
195(48)
6.1 Background
195(2)
6.2 Formulation of the Natural Gas Cash-Out Model as a Mixed-Integer Bilevel Optimization Problem
197(5)
6.2.1 The NGSC Model
198(1)
6.2.2 The TSO Model
199(3)
6.2.3 The Bilevel Model
202(1)
6.3 Approximation to a Continuous Bilevel Problem
202(1)
6.4 A Direct Solution Approach
203(1)
6.4.1 Linear TSO Objective Function
204(1)
6.5 A Penalty Function Approach to Solve the Natural Gas Cash-Out Problem
204(3)
6.6 An Expanded Problem and Its Linearization
207(14)
6.6.1 Upper Level Expansion
208(1)
6.6.2 Lower Level Expansion
209(2)
6.6.3 Linearization of the Expanded NGSC Model
211(10)
6.7 Numerical Results
221(1)
6.8 Bilevel Stochastic Optimization to Solve an Extended Natural Gas Cash-Out Problem
221(7)
6.9 Natural Gas Market Classification Using Pooled Regression
228(15)
6.9.1 Natural Gas Price-Consumption Model
229(2)
6.9.2 Regression Analysis
231(2)
6.9.3 Dendrogram-GRASP Grouping Method (DGGM)
233(4)
6.9.4 Experimental Results
237(6)
7 Applications to Other Energy Systems
243(46)
7.1 Consistent Conjectural Variations Equilibrium in a Mixed Oligopoly in Electricity Markets
243(23)
7.1.1 Introduction
243(4)
7.1.2 Model Specification
247(2)
7.1.3 Exterior Equilibrium
249(4)
7.1.4 Interior Equilibrium
253(9)
7.1.5 Numerical Results
262(4)
7.2 Toll Assignment Problems
266(23)
7.2.1 Introduction
267(5)
7.2.2 TOP as a Bilevel Optimization Model
272(1)
7.2.3 The Algorithm
273(7)
7.2.4 Results of Numerical Experiments
280(5)
7.2.5 Supplementary Material
285(4)
8 Reduction of the Dimension of the Upper Level Problem in a Bilevel Optimization Model
289(20)
8.1 Introduction
289(1)
8.2 An Example
290(2)
8.3 Relations Between Bilevel Problems (P1) and (MP1)
292(2)
8.4 An Equivalence Theorem
294(3)
8.5 Examples and Extensions
297(12)
8.5.1 The Nonlinear Case
297(3)
8.5.2 The Linear Case
300(2)
8.5.3 Normalized Generalized Nash Equilibrium
302(7)
References 309(14)
Index 323
Stephan Dempe studied mathematics at the Technische Hochschule Karl-Marx-Stadt and got a PhD from the same university. Today he is professor for mathematical optimization at the TU Bergakademie Freiberg, Germany.  Focus of his work is on parametric and nonconvex optimization.

Vyacheslav Kalashnikov studied mathematics at Novosibirsk State University, he got his PhD in Operations Research from the Siberian Division of the Academy of Sciences of the USSR and his Dr.Sc. (Habilitation degree) from the Central Economics and Mathematics Institute (CEMI), Moscow, Russia. Today he is Professor at Tecnológico de Monterrey, Mexico, at the CEMI, and at Sumy State University, Ukraine. The main areas of his work are bilevel programming,  hierarchical games and their applications in engineering and economics.

Gerardo Alfredo Perez Valdes studied mathematics at the Universidad Autónoma de Nuevo León and got his PhDs in Engineering from Tecnológico de Monterrey, Mexico, and from Texas Tech University, Lubbock, USA. Today he is Professor at University of Science and Technology in Trondheim (NTNU), Norway. The focus of his work is on solution algorithms in mathematical optimization.

Nataliya Kalashnykova studied mathematics at Novosibirsk State University and got her PhD in Operations Research from the Siberian Division of the Academy of Sciences of the USSR. Today she is Professor at the Universidad Autónoma de Nuevo León, Mexico, and at Sumy State University, Ukraine. Her expertise lies in stochastic optimal control and mathematical models of optimization.