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Dynamic system for solving saddle point problems in Hilbert spaces and its application to neural computing

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3 Author(s)
Shen, Xisheng ; MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China; Department of Automation, Tsinghua University, Beijing 100084, China ; Wang, Xiaofang ; Chai, Yueting

This paper studies the existence and uniqueness of solutions and the stability and convergence of a dynamic system for solving saddle point problems (SPP) in Hilbert spaces. The analysis first converts the SPP into a problem of searching for equilibriums of a dynamic system using a criterion for solutions of the SPP, then shows the existence and uniqueness of the solutions by creating a positive function whose Fréchet derivative is decreasing along any solution. The construction of positively invariant subsets gives the global stability and convergence of this dynamic system, that is, the dynamic system globally converges to some exact solution of the SPP. Finally, the paper also shows that the obtained results can be applied to neural computing for solving SPP.

Published in:

Tsinghua Science and Technology  (Volume:16 ,  Issue: 3 )

Date of Publication:

June 2011

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