A neurodynamic optimization approach for complex-variables programming problem.

Area of Science:

• Computational mathematics
• Optimization theory
• Neural network applications

Background:

• Convex programming with complex variables presents significant computational challenges.
• Existing methods often require complex parameter tuning, limiting practical application.
• Developing efficient and robust algorithms for this domain is crucial.

Purpose of the Study:

• To design a novel neural network model for solving complex-variable convex programming problems.
• To establish the chain rule for real-valued functions involving complex variables.
• To demonstrate a model that simplifies practical implementation by eliminating the need for penalty parameters.

Main Methods:

• Development of a neural network model based on differential inclusion.
• Establishment of the chain rule for real-valued functions with complex variables.
• Theoretical analysis of state convergence to the feasible region and optimal solutions.

Main Results:

• The designed neural network model reaches the feasible region in finite time.
• Convergence of the model's state to an optimal solution is mathematically proven.
• The model's effectiveness is validated through several typical examples.

Conclusions:

• The proposed neural network model offers an effective and simplified approach to complex-variable convex programming.
• The finite-time convergence and proven optimality ensure practical utility.
• This work contributes a valuable tool for optimization problems in complex domains.