报 告 人：殷俊峰，同济大学

邀 请 人：宋彩芹

报告时间：2026年11月6日（星期五）11:00-12:00

报告地点：7JC216

报告摘要：

We study randomized row-action methods for problems with linear observations, convex constraints, and non-Euclidean geometry. Our starting point is a unified formulation in which the data-fitting term acts in observation space, while the feasible set and the regularizer encode structure in variable space. It covers constrained least squares, nonnegative and simplex constrained models, regularized data fitting, and equality-constrained Bregman selection problems.  The structure of these problems leads naturally to two algorithmic branches. The first uses primal Bregman-proximal row steps for soft data-fitting problems. The second uses dual Bregman–Kaczmarz steps for problems with hard equality constraints. We first derive a common one-step inequality. We then give deterministic and stochastic convergence results for the soft branch under relative smoothness. For constrained least squares, the normalized row oracle has exact first- and second moment identities. They yield an expected ergodic bound in the inconsistent case, an O(1/K) bound in the interpolating case, and linear convergence of the actual iterates under a residual error bound. For equality-constrained selectors, we prove linear convergence in expected Bregman distance under a residual-to-Bregman error bound. We recall global sufficient conditions for this bound and derive local constants for the nonnegative quadratic geometry and the entropy geometry on the simplex. Numerical experiments illustrate the noisy stepsize trade-off and the local entropy selector theory, and show that entropic row-action updates can recover interpretable factors in a simplex-structured nonnegative matrix factorization problem。

报告人简介：

殷俊锋，同济大学成人论坛 教授，博导。主要研究方向数值代数与科学计算，计算金融，大数据和人工智能。主持及参与国家自然科学基金、上海市及教育部等科研项目10余项，发表高水平SCI学术论文多篇，2009年入选上海市“浦江人才”,2010年荣获中国数学会计算数学分会应用数值代数奖，2019年获中国数学会计算数学分会青年创新奖(提名)，现为中国工业与应用数学学会副秘书长，中国工业与应用数学学会大数据与人工智能专业委员会委员，中国高等教育学会教育数学委员会常务理事。