A computational approach for thermo-elasto-plastic frictional contact based on a monolithic formulation using non-smooth nonlinear complementarity functions

In this paper, a double nonmonotone quasi-Newton method is proposed for the nonlinear complementarity problem. By using 3-1 piecewise and 4-1 piecewise nonlinear complementarity functions, the nonlinear complementarity problem is reformulated into a smooth equation. By a double nonmonotone line search, a smooth Broyden-like algorithm is proposed, where a single solution of a smooth equation at each iteration is required with the reduction in the scale of the calculation. Under suitable conditions, the global convergence of the algorithm is proved, and numerical results with some practical applications are given to show the efficiency of the algorithm.

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On Generalized Convexity of Nonlinear Complementarity Functions

Journal of Optimization Theory and Applications ◽

10.1007/s10957-014-0553-3 ◽

2014 ◽

Vol 164 (2) ◽

pp. 723-730 ◽

Cited By ~ 6

Author(s):

S. Mohsen Miri ◽

Sohrab Effati

Keyword(s):

Generalized Convexity ◽

Nonlinear Complementarity ◽

Complementarity Functions

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A local Jacobian smoothing method for solving Nonlinear Complementarity Problems

Universitas Scientiarum ◽

10.11144/javeriana.sc25-1.aljs ◽

2020 ◽

Vol 25 (1) ◽

pp. 149-174

Author(s):

Favian E Arenas ◽

Héctor Jairo Martínez ◽

Rosana Pérez

Keyword(s):

Complementarity Problem ◽

Complementarity Problems ◽

Nonlinear Complementarity Problem ◽

Smoothing Method ◽

System Of Equations ◽

Nonlinear Complementarity ◽

Complementarity Functions ◽

Type Algorithm ◽

Numerical Performance ◽

Generalized Newton

In this paper, we present a smoothing of a family of nonlinear complementarity functions and use its properties in combination with the smooth Jacobian strategy to present a new generalized Newton-type algorithm to solve a nonsmooth system of equations equivalent to the Nonlinear Complementarity Problem. In addition, we prove that the algorithm converges locally and q-quadratically, and analyze its numerical performance.

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Least Change Secant Update Methods for Nonlinear Complementarity Problem

Ingeniería y Ciencia ◽

10.17230/ingciencia.11.21.1 ◽

2015 ◽

Vol 11 (21) ◽

pp. 11-21 ◽

Cited By ~ 2

Author(s):

Favián Arenas A ◽

Héctor J Martínez ◽

Rosana Pérez M

Keyword(s):

Superlinear Convergence ◽

Complementarity Problem ◽

Numerical Experiments ◽

Complementarity Problems ◽

Nonlinear Complementarity Problem ◽

Nonlinear Complementarity ◽

Complementarity Functions ◽

The One ◽

Local And Superlinear Convergence ◽

Parametric Class

In this work, we introduce a family of Least Change Secant Update Methods for solving Nonlinear Complementarity Problems based on its reformulation as a nonsmooth system using the one-parametric class of nonlinear complementarity functions introduced by Kanzow and Kleinmichel. We prove local and superlinear convergence for the algorithms. Some numerical experiments show a good performance of this algorithm.

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A One-Step Smoothing Newton Method Based on a New Class of One-Parametric Nonlinear Complementarity Functions for P 0-NCP

Advances in Neural Networks - ISNN 2010 - Lecture Notes in Computer Science ◽

10.1007/978-3-642-13278-0_15 ◽

2010 ◽

pp. 110-117

Author(s):

Liang Fang ◽

Xianming Kong ◽

Xiaoyan Ma ◽

Han Li ◽

Wei Zhang

Keyword(s):

Newton Method ◽

Smoothing Newton Method ◽

Nonlinear Complementarity ◽

New Class ◽

Complementarity Functions ◽

One Step

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Application of Modified Bloch Waves to Image Analysis of Extended Linear Defects

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010005202x ◽

1974 ◽

Vol 32 ◽

pp. 402-403

Author(s):

S. Nakahara ◽

D. M. Maher

Keyword(s):

Image Analysis ◽

Computational Approach ◽

Dislocation Loops ◽

Plane Wave Expansion ◽

Dynamical Equations ◽

Bloch Waves ◽

Linear Defects ◽

Imperfect Crystal ◽

Localized Defects ◽

Defective Crystals

Since Head first demonstrated the advantages of computer displayed theoretical intensities from defective crystals, computer display techniques have become important in image analysis. However the computational methods employed resort largely to numerical integration of the dynamical equations of electron diffraction. As a consequence, the interpretation of the results in terms of the defect displacement field and diffracting variables is difficult to follow in detail. In contrast to this type of computational approach which is based on a plane-wave expansion of the excited waves within the crystal (i.e. Darwin representation ), Wilkens assumed scattering of modified Bloch waves by an imperfect crystal. For localized defects, the wave amplitudes can be described analytically and this formulation has been used successfully to predict the black-white symmetry of images arising from small dislocation loops.

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