A neural network based on the generalized Fischer–Burmeister function for nonlinear complementarity problems

Chen, Jein Shan; Ko, Chun-Hsu; Pan, Shaohua

doi:10.1016/j.ins.2009.11.014

Cited by 43 publications

(14 citation statements)

References 32 publications

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“…In addition, its geometric view is depicted in [27] and the effect of perturbing p for different kinds of algorithms are investigated in [4,5,[7][8][9]. More recently, a generalization of natural residual function, denoted by φ p NR , is proposed in [6] and defined as…”

Section: Motivationmentioning

confidence: 99%

Symmetrization of generalized natural residual function for NCP

Chang

Chen

Yang

2015

Operations Research Letters

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Section: Motivationmentioning

confidence: 99%

Symmetrization of generalized natural residual function for NCP

Chang

Chen

Yang

2015

Operations Research Letters

Self Cite

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“…For decades, the NCP has attracted a lot of attention because of its wide applications. Consequently various methods [32][33][34] have been developed to solve the NCP. One of the most powerful and popular methods is to reformulate the NCP as a nonlinear system of equations [35].…”

Section: Complementarity Problemmentioning

confidence: 99%

A nonlinear complementarity approach for elastoplastic problems by BEM without internal cells

Deng¹,

Li²,

Wang³

et al. 2011

Engineering Analysis with Boundary Elements

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“…In other words, (w) given in (9) is a smooth merit function for the KKT system (5). Based on the above smooth minimization problem (9), it is natural to propose the first neural network for solving the KKT system (5) of SOCCVI problem:…”

Section: Lemma 31 Let φ εmentioning

confidence: 99%

“…Then, (w) ≥ 0 for w = (ε, x, μ, λ) ∈ R 1+n+l+m and (w) = 0 if and only if (x, μ, λ) solves the KKT system (5).…”

Section: Remark 31mentioning

confidence: 99%

Neural networks for solving second-order cone constrained variational inequality problem

Sun

Chen

2010

Comput Optim Appl

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In this paper, we consider using the neural networks to efficiently solve the second-order cone constrained variational inequality (SOCCVI) problem. More specifically, two kinds of neural networks are proposed to deal with the Karush-KuhnTucker (KKT) conditions of the SOCCVI problem. The first neural network uses the Fischer-Burmeister (FB) function to achieve an unconstrained minimization which is a merit function of the Karush-Kuhn-Tucker equation. We show that the merit function is a Lyapunov function and this neural network is asymptotically stable. The second neural network is introduced for solving a projection formulation whose solutions coincide with the KKT triples of SOCCVI problem. Its Lyapunov stability and global convergence are proved under some conditions. Simulations are provided to show effectiveness of the proposed neural networks.

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A neural network based on the generalized Fischer–Burmeister function for nonlinear complementarity problems

Cited by 43 publications

References 32 publications

Symmetrization of generalized natural residual function for NCP

Symmetrization of generalized natural residual function for NCP

A nonlinear complementarity approach for elastoplastic problems by BEM without internal cells

Neural networks for solving second-order cone constrained variational inequality problem

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