scholarly journals A Superlinearly Convergent Method for the Generalized Complementarity Problem over a Polyhedral Cone

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Fengming Ma ◽  
Gang Sheng ◽  
Ying Yin
Keyword(s):  
Complementarity Problem ◽  
Polyhedral Cone ◽  
System Of Equations ◽  
Equivalent System ◽  
Type Method ◽  
Linear System Of Equations ◽  
Generalized Complementarity Problem ◽  
Convergence Results ◽  
Convergent Method ◽  
Weaker Conditions

Making use of a smoothing NCP-function, we formulate the generalized complementarity problem (GCP) over a polyhedral cone as an equivalent system of equations. Then we present a Newton-type method for the equivalent system to obtain a solution of the GCP. Our method solves only one linear system of equations and performs only one line search at each iteration. Under mild assumptions, we show that our method is both globally and superlinearly convergent. Compared to the previous literatures, our method has stronger convergence results under weaker conditions.

scholarly journals An Improvement of Global Error Bound for the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hongchun Sun ◽  
Yiju Wang ◽  
Houchun Zhou ◽  
Shengjie Li
Keyword(s):  
Error Bound ◽  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Global Error ◽  
New Technique ◽  
Global Error Bound ◽  
Nonlinear Complementarity ◽  
A New Technique ◽  
Weaker Conditions

We consider the global error bound for the generalized nonlinear complementarity problem over a polyhedral cone (GNCP). By a new technique, we establish an easier computed global error bound for the GNCP under weaker conditions, which improves the result obtained by Sun and Wang (2013) for GNCP.

scholarly journals A Sharper Global Error Bound for the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Hongchun Sun ◽  
Yiju Wang
Keyword(s):  
Error Bound ◽  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Global Error ◽  
Global Error Bound ◽  
Equivalent Formulation ◽  
Nonlinear Complementarity ◽  
Weaker Conditions ◽  
Bound Estimation

We revisit the global error bound for the generalized nonlinear complementarity problem over a polyhedral cone (GNCP). By establishing a new equivalent formulation of the GNCP, we establish a sharper global error bound for the GNCP under weaker conditions, which improves the existing error bound estimation for the problem.

scholarly journals An efficient convergent method for the delay reaction-diffusion equations

2021 ◽  
Author(s):  
Marzieh Heidari ◽  
Mehdi Ghovatmand ◽  
Mohammad Hadi Noori Skandari
Keyword(s):  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
System Of Equations ◽  
Equivalent System ◽  
Numerical Examples ◽  
Delay Function ◽  
Mild Conditions ◽  
Convergent Method

In this manuscript, we consider the delay reaction-diffusion equation and implement an efficient spectral collocation method to approximate the solution of this equation. We first replace the delay function in the delay reaction-diffusion equation and achieve an equivalent system of equations. We then utilize the Legendre-Gauss-Lobatto and two-dimensional interpolating polynomial to approximate the solution of obtained system. Moreover, we prove the convergent of method under some mild conditions. Finally, the capability and efficiency of the method is illustrated by providing several numerical examples and comparing them with others

On an application of the complex nonlinear complementarity problem

1976 ◽  
Vol 15 (1) ◽  
pp. 141-148 ◽  
Author(s):  
J. Parida ◽  
B. Sahoo
Keyword(s):  
Minimization Problem ◽  
Complementarity Problem ◽  
Complex Space ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Polyhedral Cones ◽  
Existence Of A Solution ◽  
Nonlinear Complementarity

A theorem on the existence of a solution under feasibility assumptions to a convex minimization problem over polyhedral cones in complex space is given by using the fact that the problem of solving a convex minimization program naturally leads to the consideration of the following nonlinear complementarity problem: given g: Cn → Cn, find z such that g(z) ∈ S*, z ∈ S, and Re〈g(z), z〉 = 0, where S is a polyhedral cone and S* its polar.

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