报 告 人：韩德仁 教授
报告题目：Non-convex Pose Graph Optimization in SLAM via Proximal Linearized Riemannian ADMM
报告时间：2024年11月4日(周一)上午9：30
报告地点：静远楼1508会议室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
韩德仁，教授，博士生导师，现任北京航空航天大学数学科学学院院长。从事大规模优化问题、变分不等式问题的数值方法的研究工作，以及优化和变分不等式问题在交通规划、磁共振成像中的应用，发表多篇学术论文。曾获中国运筹学会青年科技奖，江苏省科学技术奖等奖项；主持国家自然科学基金杰出青年基金项目、重点项目等。担任中国运筹学会常务理事；《数值计算与计算机应用》、《Journal of the Operations Research Society of China》、《Journal of Global Optimization》、《Asia-Pacific Journal of Operational Research》编委。
报告摘要：
Pose graph optimization (PGO) is a well-known technique for solving the pose-based simultaneous localization and mapping (SLAM) problem. In this paper, we represent the rotation and translation by a unit quaternion and a three-dimensional vector, and propose a new PGO model based on the von Mises-Fisher distribution. The constraints derived from the unit quaternions are spherical manifolds, and the projection onto the constraints can be calculated by normalization. Then a proximal linearized Riemannian alternating direction method of multipliers (PieADMM) is developed to solve the proposed model, which not only has low memory requirements, but also can update the poses in parallel. Furthermore, we establish the iteration complexity of O(1/ε²) of PieADMM for finding an ϵ-stationary solution of our model. The efficiency of our proposed algorithm is demonstrated by numerical experiments on two synthetic and four 3D SLAM benchmark datasets.