Growth behavior of a class of merit functions for the nonlinear complementarity problem

1996 ◽  
Vol 89 (1) ◽  
pp. 17-37 ◽  
Author(s):  
P. Tseng
Keyword(s):  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Growth Behavior ◽  
Merit Functions ◽  
Nonlinear Complementarity

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.

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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