报告人简介

1997年获东北大学工学博士学位。1986年加入泰山学院，1994年晋升为副教授，1999年加入山东大学控制科学与工程学院，同年晋升为教授，2006年当选山东省首批“泰山学者”，2008年获得国家杰出青年基金。现为山东科技大学自动化学院特聘教授。张焕水教授研究方向为最优控制理论，随机系统，时滞系统，分布式/分散式最优控制，博弈控制以及优化理论。曾担任IEEE Trans. on Automatic Control等国内外多家期刊编委。

报告摘要

Optimization plays a crucial role in applied mathematics and is also an important scientific foundation in engineering and information fields. The development of optimization theory has a history of several hundred years, during which classic algorithms such as gradient descent, improved gradient descent, Newton method, and enhanced quasi-Newton methods have emerged. Although these algorithms have their own advantages, they also have limitations: gradient descent is stable but often converges slowly, while Newton iteration converges quickly but is prone to divergence, and its improved versions also have similar problems. This report presents a new optimization algorithm that combines fast convergence and stability. Its core idea stems from the optimal control principle (OCP). This algorithm regards the update step size during the iterative process as a control input. By designing this input to minimize the sum of the objective function and control energy at future times, the algorithm ensures the fastest convergence while minimizing the control energy to guarantee stability. Through approximation processing using Taylor expansion, this algorithm is further transformed into an iterative form, thus avoiding the complexity of solving nonlinear forward-backward difference equations. Rigorous theoretical analysis shows that this algorithm can achieve superlinear convergence similar to Newton iteration, while maintaining the stability of gradient descent. In addition, this algorithm can cover gradient descent, Newton method, improved accelerated gradient descent, and regularized Newton method, thereby providing a unified theoretical framework for these algorithms in the mathematical domain. The report concludes with the successful applications of OCP in intelligent vehicle trajectory tracking, 3D image restoration, power system power flow calculation, large-scale deep learning, and other fields.