報 告 人：韓德仁 教授

報告題目：Non-convex Pose Graph Optimization in SLAM via Proximal Linearized Riemannian ADMM

報告時間：2024年11月4日(周一)上午9：30

報告地點：靜遠樓1508會議室

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

       韓德仁，教授，博士生導師，現任北京航空航天大學數學科學學院院長。從事大規模優化問題、變分不等式問題的數值方法的研究工作，以及優化和變分不等式問題在交通規劃、磁共振成像中的應用，發表多篇學術論文。曾獲中國運籌學會青年科技獎，江蘇省科學技術獎等獎項；主持國家自然科學基金杰出青年基金項目、重點項目等。擔任中國運籌學會常務理事；《數值計算與計算機應用》、《Journal of the Operations Research Society of China》、《Journal of Global Optimization》、《Asia-Pacific Journal of Operational Research》編委。

報告摘要：

       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 ?-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.