报告人：刘勇进 （福州大学 教授）
报告时间：2023年3月26日(周日)下午2:30
报告地点：集美大学理学院章辉楼445
联系人：计算数学和概率统计团队
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报告摘要：The density matrix least squares problem arises from the quantum state tomography problem in experimental physics and has many applications in signal processing and machine learning, mainly including the phase recovery problem and the matrix completion problem. In this paper, we first reformulate the density matrix least squares problem as an equivalent convex optimization problem and then design an efficient semismooth Newton-based augmented Lagrangian (Ssnal) algorithm to solve the dual of its equivalent form, in which an inexact semismooth Newton (Ssn) algorithm with superlinear or even quadratic convergence is applied to solve the inner subproblems. Theoretically, the global convergence and locally asymptotically superlinear convergence of the Ssnal algorithm are established under very mild conditions. Computationally, the costs of the Ssn algorithm for solving the subproblem are significantly reduced by making full use of low-rank or high-rank property of optimal solutions of the density matrix least squares problem. In order to verify the performance of our algorithm, numerical experiments conducted on randomly generated quantum state tomography problems and density matrix least squares problems with real data demonstrate that the Ssnal algorithm is more effective and robust than the Qsdpnal solver and several state-of-the-art first-order algorithms.
报告人简介：福州大学数学与统计学院教授、博士生导师、院长，福建省省级人才，担任福建省应用数学中心（福州大学）主任。研究兴趣主要包括：最优化理论、方法与应用，大规模数值计算，统计优化等，研究成果在包括Mathematical Programming (Series A)、SIAM Journal on Optimization、SIAM Journal on Scientific Computing等优化与计算国际顶级学术期刊上发表。主持国家自然科学基金4项（面上项目3项、青年基金1项），主持其他部省级纵向科研项目5项。现任中国统计学会理事、中国运筹学会学术交流委员会委员、中国运筹学会数学规划分会理事、中国运筹学会智能工业数据解析与优化分会理事。
