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Neural network for nonsmooth pseudoconvex optimization with general convex constraints.

Wei Bian1, Litao Ma2, Sitian Qin3

  • 1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China; Institute of Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China.

Neural Networks : the Official Journal of the International Neural Network Society
|February 23, 2018
PubMed
Summary
This summary is machine-generated.

A novel recurrent neural network solves nonsmooth, pseudoconvex optimization problems. This network converges to optimal solutions in finite time, demonstrating efficiency for dynamic portfolio optimization.

Keywords:
Differential inclusionNeural networkNonsmooth pseudoconvex optimizationSmoothing method

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Area of Science:

  • Optimization
  • Computational Neuroscience
  • Machine Learning

Background:

  • Nonsmooth and pseudoconvex optimization problems present significant challenges.
  • Recurrent neural networks offer potential for solving complex optimization tasks.

Purpose of the Study:

  • To propose a one-layer recurrent neural network for nonsmooth, pseudoconvex optimization with convex constraints.
  • To develop a regularization function independent of the feasible region information.

Main Methods:

  • A smoothing method is employed to construct a novel regularization function.
  • Theoretical analysis is used to prove existence, uniqueness, and convergence properties of the network's state.
  • Numerical simulations validate the network's performance.

Main Results:

  • The proposed neural network guarantees global existence and uniqueness of its state.
  • The network's state converges to the feasible region in finite time and subsequently to the optimal solution set.
  • The convergence to an exact optimal solution is also established.

Conclusions:

  • The developed recurrent neural network is efficient for solving a class of nonsmooth, pseudoconvex optimization problems.
  • The network shows promise for applications in dynamic portfolio optimization.
  • The proposed method offers a robust approach to complex optimization challenges.