题目：Generic Linear Convergence for Algorithms of Non-linear Least Squares over Smooth Varieties
时间：2025年5月12日（周一）下午 3: 00-4: 00
地点：数学院203
报告人：胡胜龙（国防科技大学）
邀请人：陈亮
摘要: In applications, a substantial number of problems can be formulated as non-linear least squares problems over
smooth varieties. Unlike the usual least squares problem over a Euclidean space, the non-linear least squares pr-
oblem over a variety can be challenging to solve and analyze, even if the variety itself is simple. Geometrically,
this problem is equivalent to projecting a point in the ambient Euclidean space onto the image of the given variety
under a non-linear map. It is the singularities of the image that make both the computation and the analysis diffi-
cult. In this talk, we prove that under some mild assumptions, these troublesome singularities can always be avoid-
ed. This enables us to establish a linear convergence rate for iterative sequences generated by algorithms satisfy-
ing some standard assumptions. We apply our general results to the low-rank partially orthogonal tensor approximat-
ion problem. As a consequence, we obtain the linear convergence rate for a classical APD-ALS method applied to a
generic tensor, without any further assumptions.
报告人简介：胡胜龙，国防科技大学教授，研究方向为张量计算的理论与算法及其应用。部分研究成果发表在Math Program、Num
Math、SIMAX、SIIMS、J Symb Comput等期刊。获得中国运筹学会青年科技奖、天津市数学会青年研究奖、Sci China-Math优秀论文
奖、浙江省数学会研究成果奖等。主持湖南省自然科学基金A类、国家自然科学基金和浙江省自然科学基金多项。
