Smoothing neural network for constrained non-lipschitz optimization with applications

Wei Bian, Xiaojun Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

71 Citations (Scopus)


In this paper, a smoothing neural network (SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth, nonconvex function, and a non-Lipschitz function, and the feasible set is a closed convex subset of. Using the smoothing approximate techniques, the proposed neural network is modeled by a differential equation, which can be implemented easily. Under the level bounded condition on the objective function in the feasible set, we prove the global existence and uniform boundedness of the solutions of the SNN with any initial point in the feasible set. The uniqueness of the solution of the SNN is provided under the Lipschitz property of smoothing functions. We show that any accumulation point of the solutions of the SNN is a stationary point of the optimization problem. Numerical results including image restoration, blind source separation, variable selection, and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the SNN. Comparisons with some existing algorithms show the advantages of the SNN.
Original languageEnglish
Article number6123210
Pages (from-to)399-411
Number of pages13
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number3
Publication statusPublished - 1 Dec 2012


  • Image and signal restoration
  • non-Lipschitz optimization
  • smoothing neural network
  • stationary point
  • variable selection

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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