A novel predefined-time neurodynamic approach for mixed variational inequality problems and applications

Area of Science:

• Neurodynamics
• Mathematical Optimization
• Applied Mathematics

Background:

• Mixed variational inequality problems are fundamental in optimization.
• Existing fixed-time and finite-time stability methods have limitations in flexibility.
• Neurodynamic approaches offer potential for solving complex inequalities.

Purpose of the Study:

• To introduce a novel neurodynamic approach for mixed variational inequality problems.
• To achieve convergence within a predefined-time, enhancing flexibility.
• To demonstrate the broad applicability to various mathematical optimization tasks.

Main Methods:

• A novel neurodynamic model is proposed.
• An adjustable time parameter is incorporated for predefined-time stability.
• Theoretical analysis is conducted to ensure convergence properties.

Main Results:

• The proposed method guarantees convergence to a unique solution within a predefined time.
• The approach demonstrates superior flexibility compared to fixed-time methods.
• Numerical simulations validate the method's effectiveness and feasibility.

Conclusions:

• The novel neurodynamic approach provides an effective solution for mixed variational inequality problems.
• The predefined-time stability offers enhanced flexibility and broader applicability.
• The method is extendable to nonlinear complementarity, sparse signal recovery, and game theory problems.