报告题目:A Support-Set Algorithm for Optimization Problems with Nonnegative and Orthogonal Constraints

报 告 人:刘歆 研究院（中国科学院数学与系统科学研究院）

报告时间: 3月6日(周五) 下午15：00-16：00

报告地点:广东工业大学龙洞校区行政楼610室

Abstract:  In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size n×p exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our analysis demonstrates that, by fixing the support set, the global solution of the minimization subproblem for the proximal linearization of the objective function can be computed in closed form with at most n nonzero entries. Exploiting this structural property offers a powerful avenue for dramatically enhancing computational efficiency. Guided by this insight, we propose a support-set algorithm preserving strictly the feasibility of iterates. A central ingredient is a strategically devised update scheme for support sets that adjusts the placement of nonzero entries. We establish the global convergence of the support-set algorithm to a first-order stationary point, and show that its iteration complexity required to reach an ϵ-approximate first-order stationary point is O(ϵ−2). Numerical results are strongly in favor of our algorithm in real-world applications, including nonnegative PCA, clustering, and community detection.

个人简介：刘歆，中国科学院数学与系统科学研究院研究员，博士生导师，计算数学与科学工程计算研究所副所长。主要研究方向包括流形优化、分布式优化及其在材料计算、大数据分析和机器学习等领域的应用。刘歆分别于2016年，2021年和2023年获得国家自然科学基金委优秀青年科学基金项目、杰出青年科学基金项目和科技部重点专项的资助。2024年获得中国工业与应用数学学会萧树铁应用数学奖。现担任MPC, JCM, APJOR等国内外期刊编委，《中国科学·数学》（中英文）青年编委，《计算数学》副主编；中国科学院青年创新促进会理事长；中国工业与应用数学学会秘书长；中国运筹学会常务理事；中国数学会计算数学分会常务理事。