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A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
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Related Experiment Video

Updated: Apr 18, 2026

Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

10.2K

Neural network for constrained nonsmooth optimization using Tikhonov regularization.

Sitian Qin1, Dejun Fan1, Guangxi Wu1

  • 1Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, PR China.

Neural Networks : the Official Journal of the International Neural Network Society
|January 16, 2015
PubMed
Summary

This study introduces a novel one-layer neural network for solving nonsmooth convex optimization problems using Tikhonov regularization. The network demonstrates finite-time convergence to the optimal solution with improved efficiency and reduced complexity.

Keywords:
Nonsmooth convex optimization problemsOne-layer neural networkTikhonov regularization method

Related Experiment Videos

Last Updated: Apr 18, 2026

Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

10.2K

Area of Science:

  • Computational Mathematics
  • Artificial Intelligence
  • Optimization Theory

Background:

  • Nonsmooth convex optimization problems are prevalent in various scientific and engineering fields.
  • Existing neural network approaches often require complex structures and penalty parameters.

Purpose of the Study:

  • To propose a novel one-layer neural network for solving nonsmooth convex optimization problems.
  • To approximate solutions of nonsmooth problems with strongly convex problems.
  • To demonstrate the network's convergence properties and advantages over existing methods.

Main Methods:

  • Utilizing Tikhonov regularization to transform the original problem into a strongly convex one.
  • Designing a one-layer neural network architecture.
  • Analyzing the finite-time convergence and global stability of the network states.

Main Results:

  • The optimal solution of the original problem is effectively approximated by the solution of the regularized strongly convex problem.
  • The proposed neural network converges globally to the unique optimal solution from any initial point in finite time.
  • The network exhibits lower model complexity and eliminates the need for penalty parameters.

Conclusions:

  • The presented one-layer neural network offers an effective and efficient method for solving nonsmooth convex optimization problems.
  • The Tikhonov regularization approach simplifies the problem while ensuring convergence.
  • The network's reduced complexity and parameter-free nature present significant advantages for practical applications.