Neural networks for nonlinear and mixed complementarity problems and their applications

Dang, Chuangyin; Leung, Yee; Gao, Xingbao; Chen, Kai-zhou

doi:10.1016/j.neunet.2003.07.006

Cited by 30 publications

(9 citation statements)

References 10 publications

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“…We compare our neural network model with some existing models which also work for NCP, for instance, the ones used in [6,31,32]. At first glance, the neural network models based on projection in [6,31,32] look having lower complexity.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…At first glance, the neural network models based on projection in [6,31,32] look having lower complexity. However, we observe that the difference of the numerical performance is very marginal by testing MCPLIB benchmark problems.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Since then, neural networks have been applied to various optimization problems, including linear programming, nonlinear programming, variational inequalities, and linear and nonlinear complementarity problems; see [6,8,7,15,17,18,22,24,[31][32][33][34][35]. There have been many studies on neural-network approaches to real-world problems in some other fields, such as [26,27,36].…”

Section: Introductionmentioning

confidence: 99%

“…[18,33]) and the regularized gap function (e.g. [6]). Recently, neural networks based on the FB function have been designed for linear and quadratic programming, and for nonlinear complementarity problems [8,24].…”

Section: Introductionmentioning

confidence: 99%

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

Chen

Pan

2010

Information Sciences

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Chen

Pan

2010

Information Sciences

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“…When SOCCVI problem corresponds to the KKT conditions of a convex secondorder cone program (CSOCP) problem as (4) where both h and g are linear, the above Proposition 3.1 Let : R 1+n+l+m → R + be defined as in (9). 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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Biological Neural Control

Grzywacz

Padilla

2006

Wiley Encyclopedia of Biomedical Engineering

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Neural control refers to the manipulation of inputs to particular structures of the nervous system to cause desirable output behavior. There are two kinds of neural control mechanisms, namely, closed loop and open loop. As an example of the former, the hypothalamus receives sensory information from the body to control its temperature. If the environmental temperature rises, then the hypothalamus makes the skin sweat to cool the body. This temperature control is called closed loop, because after the output behavior is modified, new sensory data are taken to see whether the output behavior should be increased or reduced. Hence, closed‐loop neural control depends on feedback information about the effects of output behavior. In contrast, the nervous system can sometimes perform open‐loop control. This form of control does not rely on feedback to correct erroneous outputs, and thus, the nervous system must rely on knowledge of system behavior to compute its output. Therefore, open‐loop neural control requires accurate models of the system. Although such control can be less precise, it has the advantage of speed, because it does not require feedback for computations. One example of open‐loop neural control occurs in the first 100 ms of the eye trying to do smooth pursuit of a target in the visual field. This period of pursuit is open loop, because no visual feedback is available because of the delays in the visual system. Thereafter, visual feedback (and other sources of information) is available to close the loop, which improves performance.

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Neural networks for nonlinear and mixed complementarity problems and their applications

Cited by 30 publications

References 10 publications

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

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

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

Biological Neural Control

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