Titlebook: Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods; Masao Fukushima,Liqun Qi Book 1999 Springer Science+Business

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A Smoothing Function and Its Applications,on. In this paper, we reconsider a smooth approximation .(., .) to .(.) and study its applications. The function .(., .) goes back to the exponential penalty function first proposed by Kort and Bertsekas and is also related to the network smooth function by Chen and Mangasarian. It is shown that lin

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On the Local Super-Linear Convergence of a Matrix Secant Implementation of the Variable Metric Proxorithm without requiring the divergence of the proximation parameters. In this paper, the local convergence theory for matrix secant versions of the VMPPA is applied to a known globally convergent version of the algorithm. It is shown under appropriate hypotheses that the resulting algorithms are lo

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A Globally Convergent Inexact Newton Method for Systems of Monotone Equations,operty of the algorithm is that the whole sequence of iterates is always globally convergent to a solution of the system without any additional regularity assumptions. Moreover, under standard assumptions the local superlinear rate of convergence is achieved. As opposed to classical globalization st

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A Smoothing Function and Its Applications,ides a global error bound for the considered VNCP. Moreover, the smoothing function proposed in this paper is used to reformulate the VNCP as a system of parameterized smooth equations. Some properties of the smoothing path are explored. The box constrained variational inequalities can also be reformulated via the smoothing function .(., .).

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Inexact Trust-Region Methods for Nonlinear Complementarity Problems,-subproblem. We show that the algorithm is well-defined for a general nonlinear complementarity problem and that it has some nice global and local convergence properties. Numerical results indicate that the new method is quite promising.