Finite-dimensional variational inequalities and complementarity problems
This two volume work presents a comprehensive treatment of the finite dimensional variational inequality and complementarity problem, covering the basic theory, iterative algorithms, and important applications. The authors provide a broad coverage of the finite dimensional variational inequality and complementarity problem beginning with the fundamental questions of existence and uniqueness of solutions, presenting the latest algorithms and results, extending into selected neighboring topics, summarizing many classical source problems, and suggesting novel application domains. This first volume contains the basic theory of finite dimensional variational inequalities and complementarity problems. This book should appeal to mathematicians, economists, and engineers working in the field. A set price of EUR 199 is offered for volume I and II bought at the same time. Please order at: [email protected]
1 online resource (2 volumes) : illustrations
9780387955803, 9780387955810, 9780387218144, 9780387218151, 0387955801, 038795581X, 0387218149, 0387218157
666928437
Cover
Preface
Table of Contents
Contents of Volume II
Acronyms
Glossary of Notation
Numbering System
1 Introduction
1.1 Problem Description
1.2 Relations Between Problem Classes
1.3 Integrability and the KKT System
1.4 Source Problems
1.5 Equivalent Formulations
1.6 Generalizations
1.7 Concluding Remarks
1.8 Exercises
1.9 Notes and Comments
2 Solution Analysis I
2.1 Degree Theory and Nonlinear Analysis
2.2 Existence Results
2.3 Monotonicity
2.4 Monotone CPs and AVIs
2.5 The VI (K, q, M) and Copositivity
2.6 Further Existence Results for CPs
2.7 A Frictional Contact Problem
2.8 Extended Problems
2.9 Exercises
2.10 Notes and Comments
3 Solution Analysis II
3.1 Bouligand Differentiable Functions
3.2 Constraint Qualifications
3.3 Local Uniqueness of Solutions
3.4 Nondegenerate Solutions
3.5 VIs on Cartesian Products
3.6 Connectedness of Solutions
3.7 Exercises
3.8 Notes and Comments
4 The Euclidean Projector and Piecewise Functions
4.1 Polyhedral Projection
4.2 Piecewise Affine Maps
4.3 Unique Solvability of AVIs
4.4 B-Differentiability under SBCQ
4.5 Piecewise Smoothness under CRCQ
4.6 Local Properties of PC1 Functions
4.7 Projection onto a Parametric Set
4.8 Exercises
4.9 Notes and Comments
5 Sensitivity and Stability
5.1 Sensitivity of an Isolated Solution
5.2 Solution Stability of B-Differentiable Equations
5.3 Solution Stability: The Case of a Fixed Set
5.4 Parametric Problems
5.5 Solution Set Stability
5.6 Exercises
5.7 Notes and Comments
6 Theory of Error Bounds
6.1 General Discussion
6.2 Pointwise and Local Error Bounds
6.3 Global Error Bounds for VIs/CPs
6.4 Monotone AVIs
6.5 Global Bounds via a Variational Principle
6.6 Analytic Problems
6.7 Identification of Active Constraints
6.8 Exact Penalization and Some Applications
6.9 Exercises
6.10 Notes and Comments
Bibliography for Volume I
Index of Definitions and Results