报告题目：A Primal-Dual Interior-Point Relaxation Method for Symmetric Cone Programming

报 告 人： 张瑞进 副教授 南开大学

报告时间：2025 年 8 月 3 日下午 16：00-17：00

报告地点：伍卓群楼三楼研讨室四

腾讯会议 ID：934-928-618

会议密码：2025

校内联系人：李欣欣 [email protected]

报告摘要：In this talk, we propose a primal-dual interior-point relaxation method for solving symmetric cone programming by employing a smoothing barrier augmented Lagrangian function. A notable advantage of this algorithm is that it does not require the iterates to remain strictly within the interior of the cone, making it particularly suitable for warm-starting. In addition, we provide an explicit solution to the Schur complement matrix. For semidefinite programming, this explicit formulation allows the complexity of forming the Schur complement matrix to match that of the Nesterov-Todd (NT) direction, which is significantly lower compared to the Alizadeh-Haeberly-Overton (AHO) or Helmberg-Kojima-Monteiro (HKM) directions. Moreover, the resulting search direction is inherently symmetric, eliminating the need for additional symmetrization, thereby enhancing computational efficiency. For second-order cone programming, we exploit the low-rank structure of the explicit solution to design an accelerated algorithm, further improving computational performance. Finally, numerical experiments are presented to demonstrate the practical effectiveness and robustness of the proposed method.

报告人简介：张瑞进于2022年在中国科学院数学与系统科学研究院获得博士学位，2022年-2024年在中国科学院国家数学与交叉科学中心从事博士后研究工作，2024年10月加入南开大学数学科学学院。主要研究兴趣为锥规划及其在工业领域的应用。