报告题目： Generic Linear Convergence for Algorithms of Non-linear Least Squares over Smooth Varieties

报 告 人：胡胜龙 教授（国防科技大学）

报告时间：2026年9月11日（星期五）15:00—15:40

报告地点：数学科学学院114（小报告厅）

校内联系人：吴佳 教授         联系方式：84708351-8415

报告摘要： 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 problem 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 difficult.  In this talk,  we prove that under some mild assumptions,  these troublesome singularities can always be avoided.  This enables us to establish a linear convergence rate for iterative sequences generated by algorithms satisfying some standard assumptions.  We apply our general results to the low-rank partially orthogonal tensor approximation 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，研究方向为非线性优化的理论与算法。部分研究成果发表在Math Program、Num Math、MOR、SIMAX、SIIMS、J Symb Comput等期刊。获得中国运筹学会青年科技奖等。入选教育部人才计划青年学者，主持国家自然科学基金、军科委、省自然科学基金多项。