A Novel Neurodynamic Approach to Constrained Complex-Variable Pseudoconvex Optimization.

Area of Science:

• Optimization Theory
• Computational Neuroscience
• Applied Mathematics

Background:

• Complex-variable pseudoconvex optimization is crucial in science and engineering.
• Existing neurodynamic methods often require penalty parameters and have higher complexity.

Purpose of the Study:

• To propose a novel neurodynamic approach for complex-variable pseudoconvex optimization with bound and linear equality constraints.
• To develop a method with enhanced efficiency, lower complexity, and fewer assumptions than existing techniques.

Main Methods:

• A neurodynamic model incorporating an efficient penalty function is presented.
• The penalty function ensures state boundedness and convergence to the feasible region.
• Theoretical analysis demonstrates the convergence of the state to an optimal point.

Main Results:

• The proposed neural network operates without explicit penalty parameters.
• The model exhibits lower complexity compared to existing neurodynamic approaches.
• Assumptions like lower boundedness of the objective function are removed, broadening applicability.

Conclusions:

• The developed neurodynamic approach offers an efficient and simplified solution for complex-variable pseudoconvex optimization.
• The method demonstrates robust convergence properties and wider applicability.
• Numerical examples and a beamforming application validate the approach's effectiveness.