An Adaptive Lagrange Neural Network for Solving Nonsmooth PseudoConvex Optimization Problems

Introduction: Nonsmooth pseudoconvex optimization problems with constraints frequently arise in scientific and engineering fields. Traditional neural network models based on penalty functions often struggle to converge and require predefined parameters. This study introduces a novel recursive neural network model designed to address these limitations. Materials and Methods: The proposed model is based on a Lagrange multiplier penalty function paradigm, enhanced with an additional penalty term for equality constraints. It features an adaptive penalty factor mechanism that allows the network to adjust dynamically without precomputed initial values. Theoretical analysis is conducted to examine the trajectory behavior of the network. Results: It is proven that the network trajectory enters the feasible region within a bounded number of iterations and converges to the set of critical points of the optimization problem. Numerical experiments further demonstrate the model’s convergence performance and computational efficiency Discussion: Compared to traditional penalty-function-based neural networks, the proposed model offers structural simplicity, stronger convergence guarantees, and eliminates the need for manually tuned penalty parameters. The extra penalty term for equality constraints plays a crucial role in ensuring solution feasibility and accuracy Conclusion: The recursive neural network model offers a robust and efficient approach for solving nonsmooth pseudoconvex optimization problems with constraints. Its adaptability and theoretical soundness make it a promising tool for complex optimization tasks in applied domains.