题目一：Efficient Global Algorithms for Transmit Beamforming Design in ISAC Systems
内容简介：In this paper, we propose a multi-input multi-output transmit beamforming optimization model for joint radar sensing and multi-user communications, where the design of the beamformers is formulated as an optimization problem whose objective is a weighted combination of the sum rate and the Cramer-Rao bound, subject to the transmit power budget. Obtaining the global solution for the formulated nonconvex problem is a challenging task, since the sum-rate maximization problem itself (even without considering the sensing metric) is known to be NP-hard. The main contributions of this paper are threefold. Firstly, we derive an optimal closed-form solution to the formulated problem in the single-user case and the multi-user case where the channel vectors of different users are orthogonal. Secondly, for the general multi-user case, we propose a novel branch and bound (B\&B) algorithm based on the McCormick envelope relaxation. The proposed algorithm is guaranteed to find the globally optimal solution to the formulated problem. Thirdly, we design a graph neural network (GNN) based pruning policy to determine irrelevant nodes that can be directly pruned in the proposed B\&B algorithm, thereby significantly reducing the number of unnecessary enumerations in it and improving its computational efficiency. Simulation results show the efficiency of the proposed vanilla and GNN-based accelerated B\&B algorithms.
报告人：王治国
报告人简介：四川大学数学学院特聘副研究员，硕士生导师，2018年获得四川大学数学学院博士学位，2018-2020年在香港中文大学（深圳）跟随罗智泉院士从事博士后研究。2021年入选四川省“天府峨眉计划”青年人才项目。主要研究方向是非凸优化和深度学习理论及其应用，在国际著名刊物IEEE TAC，TSP和Automatica等上发表20余篇论文。荣获四川省数学会第二届应用数学奖一等奖、四川省现场统计学会第二届优秀科研成果奖教师组一等奖。主持国家自然科学基金1项，四川省自然科学基金1项。承担了国家重点研发计划“变革性技术关键科学问题”重点专项和四川大学研究生教育教学改革研究项目。
题目二：Convex and Non-Convex Impulse Noise Image Restoration Models and Algorithms
内容简介：In this talk, we introduce our two recent works: (1) We propose a new two-phase method incorporating low rank, total variation, and box constraints for image deblurring with impulse noise. Numerical experiments show that low-precision solutions can be obtained quickly. However, achieving highly accurate solutions requires more iterations and computing time. (2) We present a PLADMM algorithm to solve a general nonconvex minimization problem, which is derived from image restoration with impulse noise. Numerical experiments verify the effectiveness and efficiency of the proposed algorithms.
报告人：唐玉超
报告人简介：广州大学数学与信息科学学院，教授。主要研究方向图像处理中的优化模型和算法及其应用。在研国家自然科学基金项目和省杰出青年科学基金项目各1项，主持完成国家自然科学基金地区项目和国家自然科学基金青年项目各1项。已在《CSIAM Transactions on Applied Mathematics》、《Journal of Scientific Computing》，《Inverse Problems and Imaging》、《Set-Valued and Variational Analysis》和《中国科学数学》等国内外知名期刊发表SCI收录论文30余篇。中国数学会和中国工业与应用数学学会会员。美国数学评论员（112437）。2016年9月—2017年9月，受国家留学基金委资助在美国北卡罗来纳大学教堂山分校访问研究一年。
时 间：2024年12月20日（周五）15：00 开始
地 点：石牌校区南海楼124室
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信息科学技术学院
2024年12月18日