Format:
Online-Ressource (1 online resource)
Edition:
Online-Ausg.
ISBN:
9783662458273
Series Statement:
Energy systems
Content:
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
Note:
Includes bibliographical references and index
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Preface; Acknowledgment; Contents; 1 Introduction; 1.1 The Bilevel Optimization Problem; 1.2 Possible Transformations into a One-Level Problem; 1.3 An Easy Bilevel Optimization Problem: Continuous Knapsack Problem ; 1.4 Short History of Bilevel Optimization; 1.5 Applications of Bilevel Optimization; 1.5.1 Optimal Chemical Equilibria; 1.5.2 Optimal Traffic Tolls; 1.5.3 Optimal Operation Control of a Virtual Power Plant; 1.5.4 Spot Electricity Market with Transmission Losses; 1.5.5 Discrimination Between Sets; 1.5.6 Support Vector Machines; 2 Linear Bilevel Optimization Problem
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2.1 The Model and First Properties2.2 Optimality Conditions; 2.3 Solution Algorithms; 2.3.1 Computation of a Local Optimal Solution; 2.3.2 A Global Algorithm; 3 Reduction of Bilevel Programming to a Single Level Problem; 3.1 Different Approaches; 3.2 Parametric Optimization Problems; 3.3 Convex Quadratic Lower Level Problem; 3.4 Unique Lower Level Optimal Solution; 3.4.1 Piecewise Continuously Differentiable Functions; 3.4.2 Necessary and Sufficient Optimality Conditions; 3.4.3 Solution Algorithm; 3.5 The Classical KKT Transformation; 3.5.1 Stationary Solutions; 3.5.2 Solution Algorithms
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3.6 The Optimal Value Transformation3.6.1 Necessary Optimality Conditions; 3.6.2 Solution Algorithms; 3.7 Primal KKT Transformation; 3.8 The Optimistic Bilevel Programming Problem; 3.8.1 One Direct Approach; 3.8.2 An Approach Using Set-Valued Optimization; 3.8.3 Optimality Conditions Using Convexificators; 4 Convex Bilevel Programs; 4.1 Optimality Conditions for a Simple Convex Bilevel Program; 4.1.1 A Necessary but Not Sufficient Condition; 4.1.2 Necessary Tools from Cone-Convex Optimization; 4.1.3 A Solution Algorithm
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4.2 A Penalty Function Approach to Solution of a Bilevel Variational Inequality4.2.1 Introduction; 4.2.2 An Existence Theorem; 4.2.3 The Penalty Function Method; 4.2.4 An Example; 5 Mixed-Integer Bilevel Programming Problems; 5.1 Location of Integrality Conditions in the Upper or Lower Level Problems; 5.2 Knapsack Constraints; 5.3 Weak Solution; 5.3.1 Regions of Stability; 5.3.2 Properties of the Solution Sets; 5.3.3 Extended Solution Sets; 5.3.4 Solution Functions; 5.3.5 Weak Solution Functions; 5.3.6 Optimality Conditions; 5.3.7 Computation of Optimal Solutions
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5.4 Optimality Conditions Using a Radial-Directional Derivative5.4.1 A Special Mixed-Discrete Bilevel Problem; 5.4.2 Some Remarks on the Sets ΨD(x) and mathcalR(y); 5.4.3 Basic Properties of ""0362(x); 5.4.4 The Radial-Directional Derivative; 5.4.5 Optimality Criteria Based on the Radial-Directional Derivative; 5.4.6 Optimality Criteria Using Radial Subdifferential; 5.5 An Approach Using Monotonicity Conditions of the Optimal Value Function; 5.5.1 Introduction; 5.5.2 Problem Formulation; 5.5.3 Parametric Integer Optimization Problem; 5.5.4 An Approximation Algorithm
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5.6 A Heuristic Algorithm to Solve a Mixed-Integer Bilevel Program of Type I
Additional Edition:
ISBN 3662458276
Additional Edition:
ISBN 9783662458266
Additional Edition:
ISBN 9783662458273
Additional Edition:
Erscheint auch als Druck-Ausgabe Bilevel Programming Problems : Theory, Algorithms and Applications to Energy Networks
Language:
English
URL:
Volltext
(lizenzpflichtig)
Author information:
Dempe, Stephan 1956-
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