A smoothing approximation-based adaptive neurodynamic approach for nonsmooth resource allocation problem.

Area of Science:

• Optimization Theory
• Computational Neuroscience
• Operations Research

Background:

• Nonsmooth resource allocation problems (NRAP) present significant computational challenges.
• Existing neurodynamic approaches often struggle with complex constraints and practical implementation.

Purpose of the Study:

• To propose a novel adaptive neurodynamic approach for solving nonsmooth resource allocation problems (NRAP).
• To enhance practical implementation by avoiding set-valued subgradient terms and simplifying constraint handling.

Main Methods:

• Combines smoothing approximation with multi-agent systems to create a distributed neurodynamic model.
• Employs an adaptive penalty technique to manage private inequality constraints efficiently.
• Introduces time-varying control parameters to maintain convergence during smoothing approximation.

Main Results:

• The proposed neurodynamic approach is completely distributed, leveraging multi-agent systems' parallel computing capabilities.
• Adaptive penalties eliminate the need for parameter estimation, reducing computational cost.
• Theoretical analysis confirms the convergence of the neurodynamic approach to the optimal solution of NRAP.

Conclusions:

• The developed adaptive neurodynamic approach offers a feasible and efficient solution for nonsmooth resource allocation problems.
• The method's distributed nature and simplified constraint handling facilitate practical applications.