Optimization theory serves as a pivotal scientific instrument for achieving optimal system performance, with its origins in economic applications to identify the best investment strategies for maximizing benefits. Over the centuries, from the geometric inquiries of ancient Greece to the calculus contributions by Newton and Leibniz, optimization theory has significantly advanced. The persistent work of scientists like Lagrange, Cauchy, and von Neumann has fortified its progress. The modern era has seen an unprecedented expansion of optimization theory applications, particularly with the growth of computer science, enabling more sophisticated computational practices and widespread utilization across engineering, decision analysis, and operations research. This paper delves into the profound relationship between optimization theory and deep learning, highlighting the omnipresence of optimization problems in the latter. We explore the gradient descent algorithm and its variants, which are the cornerstone of optimizing neural networks. The chapter introduces an enhancement to the SGD optimizer, drawing inspiration from numerical optimization methods, aiming to enhance interpretability and accuracy. Our experiments on diverse deep learning tasks substantiate the improved algorithm's efficacy. The paper concludes by emphasizing the continuous development of optimization theory and its expanding role in solving intricate problems, enhancing computational capabilities, and informing better policy decisions.

本研究解决了深度学习中的优化问题，提出了一种改进的随机梯度下降（SGD）优化器，借鉴了数值优化方法，以提升模型的可解释性和准确性。实验结果表明，该算法在多种深度学习任务中表现优异，显示了优化理论在复杂问题解决中的重要性和影响力。

通过优化梯度下降增强深度学习：连接数值方法与神经网络训练