Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods

1. Front Matter

   Pages i-viii

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

   • Roberto Andreani, José Mario Martínez

   Pages 1-24

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

   • Regina S. Burachik, Claudia A. Sagastizábal, B. F. Svaiter

   Pages 25-43

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

   • James V. Burke, Song Xu

   Pages 45-63

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5. Smoothing Newton Methods for Nonsmooth Dirichlet Problems

   • Xiaojun Chen, Nami Matsunaga, Tetsuro Yamamoto

   Pages 65-79

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6. Frictional Contact Algorithms Based on Semismooth Newton Methods

   • Peter W. Christensen, Jong-Shi Pang

   Pages 81-116

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7. Well-Posed Problems and Error Bounds in Optimization

   • Sien Deng

   Pages 117-126

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

   • Steven P. Dirkse, Michael C. Ferris

   Pages 127-147

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9. Merit Functions and Stability for Complementarity Problems

   • Andreas Fischer

   Pages 149-159

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10. Minimax and Triality Theory in Nonsmooth Variational Problems

    • David Yang Gao

    Pages 161-179

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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

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12. Inexact Trust-Region Methods for Nonlinear Complementarity Problems

    • Christian Kanzow, Martin Zupke

    Pages 211-233

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

    • Wu Li, John Swetits

    Pages 235-257

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14. Regularized Linear Programs with Equilibrium Constraints

    • Olvi L. Mangasarian

    Pages 259-268

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15. Reformulations of a Bicriterion Equilibrium Model

    • Patrice Marcotte

    Pages 269-291

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16. A Smoothing Function and Its Applications

    • Ji-Ming Peng

    Pages 293-316

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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

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18. Reformulation of a Problem of Economic Equilibrium

    • Alexander M. Rubinov, Bevil Glover

    Pages 335-354

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

    • Michael V. Solodov, Benav F. Svaiter

    Pages 355-369

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

    • Roman Sznajder, M. Seetharama Gowda

    Pages 371-379

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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.

• Finite
• Operations Research
• Operator
• Variable
• algorithm
• algorithms
• calculus
• equation
• function
• linear optimization
• mathematical programming
• modeling
• optimization
• programming

• Kyoto University, Kyoto, Japan

  Masao Fukushima

• The University of New South Wales, Sydney, Australia

  Liqun Qi

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