A recurrent neural network for solving a class of general variational inequalities

Area of Science:

• Computational mathematics
• Artificial intelligence
• Neural networks

Background:

• General variational inequalities (GVIs) are an extension of classical variational inequalities.
• Solving GVIs efficiently is crucial in various scientific and engineering fields.
• Existing neural network models for variational inequalities have limitations.

Purpose of the Study:

• To propose a novel recurrent neural network (NN) model for a specific class of general variational inequalities (GVIs).
• To analyze the convergence and stability properties of the proposed NN.
• To demonstrate the model's effectiveness through numerical examples.

Main Methods:

• Development of a recurrent neural network architecture tailored for GVIs.
• Mathematical proofs to establish global convergence, global asymptotic stability, and global exponential stability under varying conditions.
• Comparative analysis with existing neural network approaches, specifically modified general projection NNs.

Main Results:

• The proposed NN model is proven to be globally convergent, globally asymptotically stable, and globally exponentially stable.
• The model shows effectiveness and strong performance in numerical experiments.
• The NN offers a modified approach compared to existing general projection NNs.

Conclusions:

• The developed recurrent neural network is a viable and effective tool for solving a special class of GVIs.
• The proven stability and convergence properties highlight the model's robustness.
• This work contributes a valuable computational method for variational inequality problems.