OPTIMIZATION OF NEURAL NETWORKS USING NONLINEAR PROGRAMMING METHODS

Abstract

The goal is to develop nonlinear programming methods for optimizing neural networks in computer science, focusing on problems with nonlinear constraints and a large parameter space, to ensure accuracy in computer modeling and quantum computing.

We investigated nonlinear programming algorithms adapted to neural networks. Neural networks with support for quadratic programming, zero neural dynamics, physical laws in discrete form, and Bayesian optimization are used. It is applied to topological optimization and quantum computing with backward error propagation, matrix approximation, automatic differentiation in frameworks such as PyTorch, and Gaussian processes.

Neural networks with physical laws accelerate convergence by 40% in topological optimization. Bayesian optimization increases accuracy by 25-30% in quantum problems. Neural networks searching for valid solutions ensure 100% fulfillment of constraints. In 3D printing, strength has increased by 15-20%, failure prediction has reached 92% accuracy, microgrids have increased efficiency by 18%, binary neural networks have improved solutions by 12-15%.

A comprehensive approach integrating quadratic programming, null neural dynamics, Bayesian optimization, and networks with search for admissible solutions for efficient optimization with constraint guarantee was developed.

The methods solve problems with millions of parameters, improving material strength, prediction accuracy, design speed by 5-8 times, and computing efficiency in microgrids. Nonlinear programming methods increase the efficiency of neural network optimization. Limitations: high computational complexity and hyperparameter settings. Prospects: scalable algorithms, meta-learning, quantum optimization, adaptation to large language models.