題目一：Efficient Global Algorithms for Transmit Beamforming Design in ISAC Systems
内容簡介：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.
報告人：王治國
報告人簡介：四川大學數學學院特聘副研究員，碩士生導師，2018年獲得四川大學數學學院博士學位，2018-2020年在香港中文大學（深圳）跟随羅智泉院士從事博士後研究。2021年入選四川省“天府峨眉計劃”青年人才項目。主要研究方向是非凸優化和深度學習理論及其應用，在國際著名刊物IEEE TAC，TSP和Automatica等上發表20餘篇論文。榮獲四川省數學會第二屆應用數學獎一等獎、四川省現場統計學會第二屆優秀科研成果獎教師組一等獎。主持國家自然科學基金1項，四川省自然科學基金1項。承擔了國家重點研發計劃“變革性技術關鍵科學問題”重點專項和四川大學研究生教育教學改革研究項目。
題目二：Convex and Non-Convex Impulse Noise Image Restoration Models and Algorithms
内容簡介：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.
報告人：唐玉超
報告人簡介：廣州大學數學與信息科學學院，教授。主要研究方向圖像處理中的優化模型和算法及其應用。在研國家自然科學基金項目和省傑出青年科學基金項目各1項，主持完成國家自然科學基金地區項目和國家自然科學基金青年項目各1項。已在《CSIAM Transactions on Applied Mathematics》、《Journal of Scientific Computing》，《Inverse Problems and Imaging》、《Set-Valued and Variational Analysis》和《中國科學數學》等國内外知名期刊發表SCI收錄論文30餘篇。中國數學會和中國工業與應用數學學會會員。美國數學評論員（112437）。2016年9月—2017年9月，受國家留學基金委資助在美國北卡羅來納大學教堂山分校訪問研究一年。
時 間：2024年12月20日（周五）15：00 開始
地 點：石牌校區南海樓124室
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2024年12月18日