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Complementarity: Applications, Algorithms and Extensions

  • Book
  • © 2001

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Editors:
  1. Michael C. Ferris

    1. Computer Sciences Department, University of Wisconsin, Madison, USA

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  2. Olvi L. Mangasarian

    1. Computer Sciences Department, University of Wisconsin, Madison, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Jong-Shi Pang

    1. Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, USA

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Part of the book series: Applied Optimization (APOP, volume 50)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-viii
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  2. Approximating Maximum Stable Set and Minimum Graph Coloring Problems with the Positive Semidefinite Relaxation

    • S. J. Benson, Y. Ye
    Pages 1-17

  3. Nonmonotone Path Following Methods for Nonsmooth Equations and Complementarity Problems

    • Stephen C. Billups, Adam L. Speight, Layne T. Watson
    Pages 19-41

  4. Scalable Probabilistic Clustering

    • P. S. Bradley, U. M. Fayyad, C. A. Reina
    Pages 43-65

  5. A Complementarity Eigenproblem in the Stability Analysis of Finite Dimensional Elastic Systems with Frictional Contact

    • A. Pinto da Costa, I. N. Figueiredo, J. J. Júdice, J. A. C. Martins
    Pages 67-83

  6. Variational Inequality Models of Restructured Electricity Systems

    • Olivier Daxhelet, Yves Smeers
    Pages 85-120

  7. Optimization Approaches to Semi-Supervised Learning

    • Ayhan Demiriz, Kristin P. Bennett
    Pages 121-141

  8. Preprocessing Complementarity Problems

    • Michael C. Ferris, Todd S. Munson
    Pages 143-164

  9. On the Connectedness of Solution Sets of Parametrized Equations and of Solution Sets in Linear Complementarity Problems

    • M. Seetharama Gowda, G. S. R. Murthy, T. Parthasarathy
    Pages 165-177

  10. An Active Set-Type Newton Method for Constrained Nonlinear Systems

    • Christian Kanzow
    Pages 179-200

  11. Mathematical Programming in Engineering Mechanics: Some Current Problems

    • G. Maier, G. Bolzon, F. Tin-Loi
    Pages 201-231

  12. Data Discrimination via Nonlinear Generalized Support Vector Machines

    • O. L. Mangasarian, David R. Musicant
    Pages 233-251

  13. On Constraint Qualifications for Mathematical Programs with Mixed Complementarity Constraints

    • J. V. Outrata
    Pages 253-271

  14. A Generation Operation Planning Model in Deregulated Electricity Markets Based on the Complementarity Problem

    • Michel Rivier, Mariano Ventosa, Andrés Ramos, Francisco Martínez-Córcoles, Ángel Chiarri Toscano
    Pages 273-295

  15. A Class of Globally Convergent Algorithms for Pseudomonotone Variational Inequalities

    • M. V. Solodov
    Pages 297-315

  16. Successive Convex Relaxation Approach to Bilevel Quadratic Optimization Problems

    • Akiko Takeda, Masakazu Kojima
    Pages 317-340

  17. On a Nonsmooth Newton Method for Nonlinear Complementarity Problems in Function Space with Applications to Optimal Control

    • Michael Ulbrich
    Pages 341-360

  18. The Proximal Point Algorithm for the P 0 Complementarity Problem

    • Nobuo Yamashita, Junji Imai, Masao Fukushima
    Pages 361-379

  19. Free Boundary Problems in Asset Pricing with Transaction Costs

    • Thaleia Zariphopoulou
    Pages 381-400

  20. Back Matter

    Pages 401-403
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Keywords

About this book

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.

Editors and Affiliations

  • Computer Sciences Department, University of Wisconsin, Madison, USA

    Michael C. Ferris, Olvi L. Mangasarian

  • Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, USA

    Jong-Shi Pang

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