Skip to main content
SpringerLink
Log in
Book cover

Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods

  • Book
  • © 1999

Overview

Editors:
  1. Masao Fukushima

    1. Kyoto University, Kyoto, Japan

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  2. Liqun Qi

    1. The University of New South Wales, Sydney, Australia

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Applied Optimization (APOP, volume 22)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (22 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Solving Complementarity Problems by Means of a New Smooth Constrained Nonlinear Solver

    • Roberto Andreani, José Mario Martínez
    Pages 1-24

  3. ε-Enlargements of Maximal Monotone Operators: Theory and Applications

    • Regina S. Burachik, Claudia A. Sagastizábal, B. F. Svaiter
    Pages 25-43

  4. A Non-Interior Predictor-Corrector Path-Following Method for LCP

    • James V. Burke, Song Xu
    Pages 45-63

  5. Smoothing Newton Methods for Nonsmooth Dirichlet Problems

    • Xiaojun Chen, Nami Matsunaga, Tetsuro Yamamoto
    Pages 65-79

  6. Frictional Contact Algorithms Based on Semismooth Newton Methods

    • Peter W. Christensen, Jong-Shi Pang
    Pages 81-116

  7. Well-Posed Problems and Error Bounds in Optimization

    • Sien Deng
    Pages 117-126

  8. Modeling and Solution Environments for MPEC: GAMS & MATLAB

    • Steven P. Dirkse, Michael C. Ferris
    Pages 127-147

  9. Merit Functions and Stability for Complementarity Problems

    • Andreas Fischer
    Pages 149-159

  10. Minimax and Triality Theory in Nonsmooth Variational Problems

    • David Yang Gao
    Pages 161-179

  11. Global and Local Superlinear Convergence Analysis of Newton-Type Methods for Semismooth Equations with Smooth Least Squares

    • Houyuan Jiang, Daniel Ralph
    Pages 181-209

  12. Inexact Trust-Region Methods for Nonlinear Complementarity Problems

    • Christian Kanzow, Martin Zupke
    Pages 211-233

  13. Regularized Newton Methods for Minimization of Convex Quadratic Splines with Singular Hessians

    • Wu Li, John Swetits
    Pages 235-257

  14. Regularized Linear Programs with Equilibrium Constraints

    • Olvi L. Mangasarian
    Pages 259-268

  15. Reformulations of a Bicriterion Equilibrium Model

    • Patrice Marcotte
    Pages 269-291

  16. A Smoothing Function and Its Applications

    • Ji-Ming Peng
    Pages 293-316

  17. On the Local Super-Linear Convergence of a Matrix Secant Implementation of the Variable Metric Proximal Point Algorithm for Monotone Operators

    • Maijian Qian, James V. Burke
    Pages 317-334

  18. Reformulation of a Problem of Economic Equilibrium

    • Alexander M. Rubinov, Bevil Glover
    Pages 335-354

  19. A Globally Convergent Inexact Newton Method for Systems of Monotone Equations

    • Michael V. Solodov, Benav F. Svaiter
    Pages 355-369

  20. On the Limiting Behavior of the Trajectory of Regularized Solutions of a P0-Complementarity Problem

    • Roman Sznajder, M. Seetharama Gowda
    Pages 371-379
Back to top

Keywords

About this book

The concept of "reformulation" has long been playing an important role in mathematical programming. A classical example is the penalization technique in constrained optimization that transforms the constraints into the objective function via a penalty function thereby reformulating a constrained problem as an equivalent or approximately equivalent unconstrained problem. More recent trends consist of the reformulation of various mathematical programming prob­ lems, including variational inequalities and complementarity problems, into equivalent systems of possibly nonsmooth, piecewise smooth or semismooth nonlinear equations, or equivalent unconstrained optimization problems that are usually differentiable, but in general not twice differentiable. Because of the recent advent of various tools in nonsmooth analysis, the reformulation approach has become increasingly profound and diversified. In view of growing interests in this active field, we planned to organize a cluster of sessions entitled "Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods" in the 16th International Symposium on Mathematical Programming (ismp97) held at Lausanne EPFL, Switzerland on August 24-29, 1997. Responding to our invitation, thirty-eight people agreed to give a talk within the cluster, which enabled us to organize thirteen sessions in total. We think that it was one of the largest and most exciting clusters in the symposium. Thanks to the earnest support by the speakers and the chairpersons, the sessions attracted much attention of the participants and were filled with great enthusiasm of the audience.

Editors and Affiliations

  • Kyoto University, Kyoto, Japan

    Masao Fukushima

  • The University of New South Wales, Sydney, Australia

    Liqun Qi

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation