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 Global Error Bound Estimation for the Generalized Nonlinear Complementarity Problem over a Closed Convex Cone

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hongchun Sun ◽  
Yiju Wang
Keyword(s):  
Error Bound ◽  
Complementarity Problem ◽  
Convex Cone ◽  
Nonlinear Complementarity Problem ◽  
Global Error ◽  
Closed Convex Cone ◽  
Global Error Bound ◽  
Nonlinear Complementarity ◽  
Bound Estimation

The global error bound estimation for the generalized nonlinear complementarity problem over a closed convex cone (GNCP) is considered. To obtain a global error bound for the GNCP, we first develop an equivalent reformulation of the problem. Based on this, a global error bound for the GNCP is established. The results obtained in this paper can be taken as an extension of previously known results.

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.

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 Existence theory for the complex nonlinear complementarity problem

1976 ◽  
Vol 14 (3) ◽  
pp. 417-423 ◽  
Author(s):  
J. Parida ◽  
B. Sahoo
Keyword(s):  
Existence Theorem ◽  
Unique Solution ◽  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Existence Theory ◽  
Polar Cone ◽  
Nonlinear Complementarity ◽  
Strongly Monotone ◽  
Image Position

The main result in this paper is an existence theorem for the following complex nonlinear complementarity problem: find z such thatwhere S is a polyhedral cone in Cn, S* the polar cone, and g is a mapping from Cn into itself. It is shown that the above problem has a unique solution if the mapping g is continuous and strongly monotone on the polyhedral cone S.

A NEURAL NETWORK FOR THE GENERALIZED NONLINEAR COMPLEMENTARITY PROBLEM OVER A POLYHEDRAL CONE

2015 ◽  
Vol 99 (3) ◽  
pp. 364-379 ◽  
Author(s):  
YIFEN KE ◽  
CHANGFENG MA
Keyword(s):  
Neural Network ◽  
Asymptotic Stability ◽  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Unconstrained Minimization ◽  
Polyhedral Cone ◽  
Nonlinear Complementarity ◽  
Trajectory Simulation ◽  
The Neural Network ◽  
Simulation Results

In this paper, we consider a neural network model for solving the generalized nonlinear complementarity problem (denoted by GNCP) over a polyhedral cone. The neural network is derived from an equivalent unconstrained minimization reformulation of the GNCP, which is based on the penalized Fischer–Burmeister function ${\it\phi}_{{\it\mu}}(a,b)={\it\mu}{\it\phi}_{\mathit{FB}}(a,b)+(1-{\it\mu})a_{+}b_{+}$. We establish the existence and the convergence of the trajectory of the neural network, and study its Lyapunov stability, asymptotic stability and exponential stability. It is found that a larger ${\it\mu}$ leads to a better convergence rate of the trajectory. Simulation results are also reported.

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