scholarly journals A generalized complementarity problem in Hilbert space

1990 ◽  
Author(s):  
Jen-Chih Yao
Keyword(s):  
Hilbert Space ◽  
Complementarity Problem ◽  
Generalized Complementarity Problem

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.

scholarly journals Generalized Complementarity Problem with Three Classes of Generalized Variational Inequalities Involving ⊕ Operation

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rais Ahmad ◽  
Iqbal Ahmad ◽  
Zahoor Ahmad Rather ◽  
Yuanheng Wang
Keyword(s):  
Variational Inequalities ◽  
Iterative Algorithm ◽  
Complementarity Problem ◽  
Convergence Result ◽  
Generalized Variational Inequalities ◽  
Generalized Complementarity Problem ◽  
Xor Operation

In this study, we introduce and study a generalized complementarity problem involving XOR operation and three classes of generalized variational inequalities involving XOR operation. Under certain appropriate conditions, we establish equivalence between them. An iterative algorithm is defined for solving one of the three generalized variational inequalities involving XOR operation. Finally, an existence and convergence result is proved, supported by an example.

scholarly journals Fixed point theory and complementarity problems in Hilbert space

1987 ◽  
Vol 36 (2) ◽  
pp. 295-310 ◽  
Author(s):  
G. Isac
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Fixed Point Theory ◽  
Point Theory

In this paper we study both the implicit and the explicit complementarity problem using some special and interesting connections between the complementarity problem and fixed point theory in Hilbert space.

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