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BL
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| Record Number
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889006
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| Title & Author
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Generalized Nash equilibrium problems, bilevel programming and MPEC /\ Didier Aussel, C.S. Lalitha, editors.
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| Publication Statement
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Singapore :: Springer,, [2018]
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, ©2018
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| Series Statement
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Forum for interdisciplinary mathematics
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| Page. NO
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1 online resource :: illustrations
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| ISBN
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9789811047749
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: 981104774X
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9789811047732
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Preface; Homage; Contents; About the Editors; 1 Bilevel Optimization: Reformulation and First Optimality Conditions; 1.1 Introduction; 1.2 Strongly Stable Lower Level Solution; 1.3 Use of the Karush-Kuhn-Tucker Conditions; 1.4 Optimal Value Function Transformation; 1.5 Exercises; References; 2 Calmness as a Constraint Qualification for M-Stationarity Conditions in MPECs; 2.1 Introduction; 2.2 Some Tools from Variational Analysis; 2.2.1 Elements of Nondifferentiable Calculus; 2.2.2 Lipschitz Properties of Set-Valued Mappings; 2.3 Calmness and Aubin Property in Optimization Problems
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2.3.1 Calmness as a Constraint Qualification for Abstract Optimization Problems2.3.2 Verification of Calmness and Aubin Property; 2.4 M-Stationarity Conditions for MPECs; 2.5 Verification of Calmness for the Perturbation Mapping; 2.5.1 Using the Aubin Property; 2.5.2 Using Polyhedrality or Structured Calmness; 2.6 Coderivative Formulae and Fully Explicit M-Stationarity Conditions; References; 3 Optimality Conditions for Bilevel Programming: An Approach Through Variational Analysis; 3.1 Introduction; 3.2 Tools from Non-smooth Analysis: A Detour; 3.3 First Look at Optimality
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3.4 Second-Order Subdifferentials: Another Detour3.5 Value Function Reformulation and Fully Convex Lower-Level Problem; 3.6 Conclusions; References; 4 Mechanism Design and Auctions for Electricity Networks; 4.1 Introduction; 4.2 Setting; 4.3 Literature; 4.4 Quantitative Formulations; 4.4.1 Generality; 4.4.2 The Standard Allocation Problem; 4.4.3 The Agent Problem; 4.4.4 The Optimal Mechanism Design Problem; 4.4.5 A Differential Equation; 4.5 Important Results; 4.6 The ISO Response for a Binodal Setting with Piecewise Linear Cost; 4.6.1 Introduction; 4.6.2 If d<barq; 4.6.3 Case dgebarq
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4.7 Ongoing Work4.8 Exercise; References; 5 Reflection Methods for Inverse Problems with Applications to Protein Conformation Determination; 5.1 Techniques of Variational Analysis; 5.2 Introduction to Reflection Methods; 5.3 Mathematical Preliminaries; 5.4 Matrix Completion; 5.5 The Douglas-Rachford Reflection Method; 5.6 Protein Conformation Determination; 5.7 Computational Experiments; 5.7.1 Basic Douglas-Rachford Algorithm Results; 5.7.2 Douglas-Rachford Algorithm with Periodic Rank Projections; 5.7.3 Reconstructions with Additional Distance Data
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5.7.4 Ionic Liquid Bulk Structure Determination5.8 Concluding Remarks; References; 6 On Single-Valuedness of Quasimonotone Set-Valued Operators; 6.1 Introduction; 6.2 Notations; 6.2.1 Basic Definitions; 6.2.2 Single-Directionality; 6.2.3 Normal Operator in Quasiconvex Optimization; 6.3 Pointwise Single-Directionality; 6.4 Local Single-Directionality; 6.4.1 General Results; 6.4.2 Application to Normal Operator; 6.5 Dense Single-Directionality; 6.5.1 General Results; 6.5.2 Dense Single-Directional Property: The Case of the Normal Operator; References
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| Subject
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Game theory.
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Game theory.
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MATHEMATICS-- Applied.
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| Subject
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MATHEMATICS-- Probability Statistics-- General.
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| Dewey Classification
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519.3
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| LC Classification
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QA269
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| Added Entry
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Aussel, Didier
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Lalitha, C. S.
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