scholarly journals ON SOME NCP-FUNCTIONS BASED ON THE GENERALIZED FISCHER–BURMEISTER FUNCTION

2007 ◽  
Vol 24 (03) ◽  
pp. 401-420 ◽  
Author(s):  
JEIN-SHAN CHEN
Keyword(s):  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Unconstrained Minimization ◽  
Merit Functions ◽  
Nonlinear Complementarity

In this paper, we study several NCP-functions for the nonlinear complementarity problem (NCP) which are indeed based on the generalized Fischer–Burmeister function, ϕp(a, b) = ||(a, b)||p - (a + b). It is well known that the NCP can be reformulated as an equivalent unconstrained minimization by means of merit functions involving NCP-functions. Thus, we aim to investigate some important properties of these NCP-functions that will be used in solving and analyzing the reformulation of the NCP.

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.

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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