Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods

ISBN-13: 9781441948052 / Angielski / Miękka / 2010 / 444 str.

Masao Fukushima; Liqun Qi

Opis

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."

Spis treści

Preface. Solving Complementarity Problems by Means of a New Smooth Constrained Nonlinear Solver; R. Andreani, J.M. Martínez.ϵ-Enlargements of Maximal Monotone Operators: Theory and Applications; R.S. Burachik, et al. A Non-Interior Predictor Corrector Path-Following Method for LCP; J.V. Burke, S. Xu.Smoothing Newton Methods for Nonsmooth Dirichlet Problems; X. Chen, etal. Frictional Contact Algorithms Based on Semismooth Newton Methods;P.W. Christensen, J.-S. Pang. Well-Posed Problems and Error Bounds in Optimization; S. Deng. Modeling and Solution Environments for MPEC: GAMS & MATLAB; S.P. Dirkse, M.C. Ferris. Merit Functions and Stability for Complementarity Problems; A. Fischer. Minimax and Triality Theory in Nonsmooth Variational Problems; D.Y. Gao. Global and Local Superlinear Convergence Analysis of Newton-Type Methods for Semismooth Equations with Smooth Least Squares; H. Jiang, D. Ralph.Inexact Trust-Region Methods for Nonlinear Complementarity Problems; C.Kanzow, M. Zupke. Regularized Newton Methods for Minimization of Convex Quadratic Splines with Singular Hessians; W. Li, J. Swetits.Regularized Linear Programs with Equilibrium Constraints; L.L.Mangasarian. Reformulations of a Bicriterion Equilibrium Model; P.Marcotte. A Smoothing Function and Its Applications; J.-M. Peng.On the Local Super-Linear Convergence of a Matrix Secant Implementation of the Variable Metric Proximal Point Algorithm for Monotone Operators; M.Qian, J.V. Burke. Reformulation of a Problem of Economic Equilibrium;A.M. Rubinov, B.M. Glover. A Globally Convergent Inexact NewtonMethod for Systems of Monotone Equations; M.V. Solodov, B.F.Svaiter. On the Limiting Behavior of the Trajectory of RegularizedSolutions of a P0&y;-Complementarity Problem;R. Sznajder, M.S.Gowda. Analysis of a Non-Interior Continuation Method Based on Chen-Mangasarian Smoothing Functions for Complementarity Problems; P.Tseng. A New Merit Function and a Descent Method for Semidefinite Complementarity Problems; N. Yamashita, M. Fukushima. Numerical Experiments for a Class of Squared Smoothing Newton Methods for Box Constrained Variational Inequality Problems; G. Zhou, et al.