Ebook: Complementarity: Applications, Algorithms and Extensions

This volume presents state-of-the-art complementarity applications, algorithms, extensions and theory in the form of eighteen papers. These at the International Conference on Com­ invited papers were presented plementarity 99 (ICCP99) held in Madison, Wisconsin during June 9-12, 1999 with support from the National Science Foundation under Grant DMS-9970102. Complementarity is becoming more widely used in a variety of appli­ cation areas. In this volume, there are papers studying the impact of complementarity in such diverse fields as deregulation of electricity mar­ kets, engineering mechanics, optimal control and asset pricing. Further­ more, application of complementarity and optimization ideas to related problems in the burgeoning fields of machine learning and data mining are also covered in a series of three articles. In order to effectively process the complementarity problems that arise in such applications, various algorithmic, theoretical and computational extensions are covered in this volume. Nonsmooth analysis has an im­ portant role to play in this area as can be seen from articles using these tools to develop Newton and path following methods for constrained nonlinear systems and complementarity problems. Convergence issues are covered in the context of active set methods, global algorithms for pseudomonotone variational inequalities, successive convex relaxation and proximal point algorithms. Theoretical contributions to the connectedness of solution sets and constraint qualifications in the growing area of mathematical programs with equilibrium constraints are also presented. A relaxation approach is given for solving such problems. Finally, computational issues related to preprocessing mixed complementarity problems are addressed.

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This volume contains a collection of papers from experts in the field of complementarity on state-of-the-art applications, algorithms, extensions and theory, resulting in a contemporary view of the complete field of complementarity.
The impact of complementarity in such diverse fields as deregulation of electricity markets, engineering mechanics, optimal control and asset pricing is described using both survey and current research articles. The papers outline problem classes where complementarity can be used to model both physical and structural phenomena in ways that lead to new solution approaches. The novel application of complementarity and optimization ideas to problems in the burgeoning fields of machine learning and data mining is covered.
New algorithmic advances including preprocessing and nonmonotone searches, extensions of computational methods using tools from nonsmooth analysis, and related theory for mathematical programs with equilibrium constraints is also detailed.
Audience: Researchers and advanced students working in optimization and management sciences.

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This volume contains a collection of papers from experts in the field of complementarity on state-of-the-art applications, algorithms, extensions and theory, resulting in a contemporary view of the complete field of complementarity.
The impact of complementarity in such diverse fields as deregulation of electricity markets, engineering mechanics, optimal control and asset pricing is described using both survey and current research articles. The papers outline problem classes where complementarity can be used to model both physical and structural phenomena in ways that lead to new solution approaches. The novel application of complementarity and optimization ideas to problems in the burgeoning fields of machine learning and data mining is covered.
New algorithmic advances including preprocessing and nonmonotone searches, extensions of computational methods using tools from nonsmooth analysis, and related theory for mathematical programs with equilibrium constraints is also detailed.
Audience: Researchers and advanced students working in optimization and management sciences.
Content:
Front Matter....Pages i-viii
Approximating Maximum Stable Set and Minimum Graph Coloring Problems with the Positive Semidefinite Relaxation....Pages 1-17
Nonmonotone Path Following Methods for Nonsmooth Equations and Complementarity Problems....Pages 19-41
Scalable Probabilistic Clustering....Pages 43-65
A Complementarity Eigenproblem in the Stability Analysis of Finite Dimensional Elastic Systems with Frictional Contact....Pages 67-83
Variational Inequality Models of Restructured Electricity Systems....Pages 85-120
Optimization Approaches to Semi-Supervised Learning....Pages 121-141
Preprocessing Complementarity Problems....Pages 143-164
On the Connectedness of Solution Sets of Parametrized Equations and of Solution Sets in Linear Complementarity Problems....Pages 165-177
An Active Set-Type Newton Method for Constrained Nonlinear Systems....Pages 179-200
Mathematical Programming in Engineering Mechanics: Some Current Problems....Pages 201-231
Data Discrimination via Nonlinear Generalized Support Vector Machines....Pages 233-251
On Constraint Qualifications for Mathematical Programs with Mixed Complementarity Constraints....Pages 253-271
A Generation Operation Planning Model in Deregulated Electricity Markets Based on the Complementarity Problem....Pages 273-295
A Class of Globally Convergent Algorithms for Pseudomonotone Variational Inequalities....Pages 297-315
Successive Convex Relaxation Approach to Bilevel Quadratic Optimization Problems....Pages 317-340
On a Nonsmooth Newton Method for Nonlinear Complementarity Problems in Function Space with Applications to Optimal Control....Pages 341-360
The Proximal Point Algorithm for the P 0 Complementarity Problem....Pages 361-379
Free Boundary Problems in Asset Pricing with Transaction Costs....Pages 381-400
Back Matter....Pages 401-403

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This volume contains a collection of papers from experts in the field of complementarity on state-of-the-art applications, algorithms, extensions and theory, resulting in a contemporary view of the complete field of complementarity.
The impact of complementarity in such diverse fields as deregulation of electricity markets, engineering mechanics, optimal control and asset pricing is described using both survey and current research articles. The papers outline problem classes where complementarity can be used to model both physical and structural phenomena in ways that lead to new solution approaches. The novel application of complementarity and optimization ideas to problems in the burgeoning fields of machine learning and data mining is covered.
New algorithmic advances including preprocessing and nonmonotone searches, extensions of computational methods using tools from nonsmooth analysis, and related theory for mathematical programs with equilibrium constraints is also detailed.
Audience: Researchers and advanced students working in optimization and management sciences.
Content:
Front Matter....Pages i-viii
Approximating Maximum Stable Set and Minimum Graph Coloring Problems with the Positive Semidefinite Relaxation....Pages 1-17
Nonmonotone Path Following Methods for Nonsmooth Equations and Complementarity Problems....Pages 19-41
Scalable Probabilistic Clustering....Pages 43-65
A Complementarity Eigenproblem in the Stability Analysis of Finite Dimensional Elastic Systems with Frictional Contact....Pages 67-83
Variational Inequality Models of Restructured Electricity Systems....Pages 85-120
Optimization Approaches to Semi-Supervised Learning....Pages 121-141
Preprocessing Complementarity Problems....Pages 143-164
On the Connectedness of Solution Sets of Parametrized Equations and of Solution Sets in Linear Complementarity Problems....Pages 165-177
An Active Set-Type Newton Method for Constrained Nonlinear Systems....Pages 179-200
Mathematical Programming in Engineering Mechanics: Some Current Problems....Pages 201-231
Data Discrimination via Nonlinear Generalized Support Vector Machines....Pages 233-251
On Constraint Qualifications for Mathematical Programs with Mixed Complementarity Constraints....Pages 253-271
A Generation Operation Planning Model in Deregulated Electricity Markets Based on the Complementarity Problem....Pages 273-295
A Class of Globally Convergent Algorithms for Pseudomonotone Variational Inequalities....Pages 297-315
Successive Convex Relaxation Approach to Bilevel Quadratic Optimization Problems....Pages 317-340
On a Nonsmooth Newton Method for Nonlinear Complementarity Problems in Function Space with Applications to Optimal Control....Pages 341-360
The Proximal Point Algorithm for the P 0 Complementarity Problem....Pages 361-379
Free Boundary Problems in Asset Pricing with Transaction Costs....Pages 381-400
Back Matter....Pages 401-403
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