A neurodynamic approach to nonsmooth constrained pseudoconvex optimization problem.

Area of Science:

• Optimization
• Computational Neuroscience
• Machine Learning

Background:

• Constrained pseudoconvex optimization is crucial in various fields.
• Existing methods often require strong assumptions on the feasible region or objective function.
• Global convergence and lower-dimensional solutions remain challenges.

Purpose of the Study:

• To introduce a new neurodynamic approach for constrained pseudoconvex optimization.
• To develop a neural network capable of global convergence and reduced solution space dimensionality.
• To overcome limitations of existing methods by relaxing common assumptions.

Main Methods:

• A novel neurodynamic model utilizing a hard comparator and piecewise linear function.
• Ensuring state solutions remain within the feasible region.
• Demonstrating convergence to optimal solutions for constrained pseudoconvex problems.

Main Results:

• The proposed neurodynamic approach achieves global convergence.
• It results in a lower dimension of the solution space compared to existing methods.
• The approach does not require assumptions like bounded feasible regions or coercive objective functions.
• Successful application demonstrated in support vector regression.

Conclusions:

• The neurodynamic approach is a viable and performant method for constrained pseudoconvex optimization.
• It offers advantages in convergence properties and reduced dimensionality.
• The method's robustness is confirmed by its performance on a real-world machine learning task.