scholarly journals Further Application ofH-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Wei-Zhe Gu ◽  
Mohamed A. Tawhid
Keyword(s):  
Stationary Point ◽  
Complementarity Problem ◽  
Global Minimum ◽  
Complementarity Problems ◽  
Merit Function ◽  
Merit Functions ◽  
Generalized Complementarity Problem ◽  
Nonlinear Complementarity ◽  
Generalized Complementarity Problems ◽  
The Given

We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) wherefandgareH-differentiable. We describeH-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on theH-differentials offandg, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP(f,g)to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved forC1, semismooth, and locally Lipschitzian.

SOME PROPERTIES OF A CLASS OF MERIT FUNCTIONS FOR SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

2006 ◽  
Vol 23 (04) ◽  
pp. 473-495 ◽  
Author(s):  
YONG-JIN LIU ◽  
LI-WEI ZHANG ◽  
YIN-HE WANG
Keyword(s):  
Error Bound ◽  
Complementarity Problems ◽  
Symmetric Cone ◽  
Merit Function ◽  
Nonlinear Complementarity Problems ◽  
Global Error ◽  
Merit Functions ◽  
Global Error Bound ◽  
Nonlinear Complementarity

In this paper, we extend a class of merit functions proposed by Kanzow et al. (1997) for linear/nonlinear complementarity problems to Symmetric Cone Complementarity Problems (SCCP). We show that these functions have several interesting properties, and establish a global error bound for the solution to the SCCP as well as the level boundedness of every merit function under some mild assumptions. Moreover, several functions are demonstrated to enjoy these properties.

scholarly journals A local Jacobian smoothing method for solving Nonlinear Complementarity Problems

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.

scholarly journals A Kind of Stochastic Eigenvalue Complementarity Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Ying-xiao Wang ◽  
Shou-qiang Du
Keyword(s):  
Complementarity Problem ◽  
Eigenvalue Problems ◽  
Complementarity Problems ◽  
Smoothing Newton Method ◽  
Convergence Properties ◽  
Eigenvalue Complementarity Problem ◽  
Interest In Research ◽  
Global And Local ◽  
The Given ◽  
Nonnegative Constraints

With the development of computer science, computational electromagnetics have also been widely used. Electromagnetic phenomena are closely related to eigenvalue problems. On the other hand, in order to solve the uncertainty of input data, the stochastic eigenvalue complementarity problem, which is a general formulation for the eigenvalue complementarity problem, has aroused interest in research. So, in this paper, we propose a new kind of stochastic eigenvalue complementarity problem. We reformulate the given stochastic eigenvalue complementarity problem as a system of nonsmooth equations with nonnegative constraints. Then, a projected smoothing Newton method is presented to solve it. The global and local convergence properties of the given method for solving the proposed stochastic eigenvalue complementarity problem are also given. Finally, the related numerical results show that the proposed method is efficient.

scholarly journals Least Change Secant Update Methods for Nonlinear Complementarity Problem

2015 ◽  
Vol 11 (21) ◽  
pp. 11-21 ◽  
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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