李林 助理教授（南华大学）

于海军 研究员

An effective minimal method tailored for general nonconvex unconstrained optimization problems

7月3日（周四）14:00-15:00，思源楼817

Unconstrained optimization problems are becoming increasingly common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been getting more and more research attention. Moreover, an efficient iterative method to minimize all kinds of objective functions is urgently needed, especially nonsmooth objective functions. In the current paper, we focus on proposing an efficient iterative method tailored for unconstrained optimization problems whether the objective function is smooth or not. To be specific, based on the variational procedure to refine the gradient and Hessian matrix approximations, an efficient quadratic model with $2n$ constrained conditions is established. Moreover, to improve the computational efficiency, a simplified model with 2 constrained conditions is first proposed, where the gradient and Hessian matrix can be explicitly updated, and the corresponding boundedness of the remaining $2n-2$ constrained conditions is also derived. On the other hand, approximation results on derivative information are also analyzed and shown. Numerical experiments including smooth, derivative blasting and nonsmooth problems are tested, where our method demonstrates significant advantages in comparison with existing methods. Furthermore, our method can also be easily translated into Matlab code. These indicate that our proposed method not also has great application prospect, but also is very meaningful to explore practical complex engineering and scientific problems.

报告人简介：李林，2017年6月博士毕业于北京科技大学，导师林平教授，研究方向为计算数学。2017年7月到至今在南华大学数理学院工作。研究内容包括谱方法、多解计算、数值优化、非线性迭代等。近年来主要以设计高精度、高效的非线性迭代多解算法为研究核心，提出了谱信赖域法、自适应正交基函数法等算法，且研究成果发表在Journal of Scientific Computing、Journal of Computational Mathematics等国际刊物上。