报告时间：2024年6月10日下午14:00
报告地点：工科4号楼638会议室
报告一题目：求解凸优化问题的自适应 Barzilai-Borwein方法
报告人：杨俊锋教授 南京大学
报告摘要：我们提出了一种基于 Barzilai-Borwein 步长的自适应梯度方法。该算法无需线搜索和参数设置，可用于求解梯度算子局部李普希茨连续的无约束凸优化问题。我们建立了点列收敛性和目标函数值的收敛速率。此外，我们将算法推广到解决复合凸优化问题和局部强凸问题。数值实验表明所提算法在一些典型算例上表现良好。
报告人简介：杨俊锋，南京大学数学系教授，博士生导师。1999年-2006年在河北师范大学数学与信息科学学院学习，获理科学士学位和硕士学位，2006年-2009年在南京大学攻读博士学位，2009年7月起在南京大学数学系工作，主要从事最优化计算方法及其应用研究，开发图像去模糊软件包FTVd, 压缩感知一模解码软件包YALL1, 核磁共振图像复原软件包RecPF等。2012 年入选教育部新世纪优秀人才支持计划, 2016年获中国运筹学会青年科技奖，2017年获国际华裔数学家联盟最佳论文奖, 2019年获国家自然科学基金优秀青年项目, 2020-2022连续三年入选爱思唯尔中国高被引学者。
报告题目二：Regularized splitting methods for the sums of maximal monotone operators and its applications
报告人：蔡邢菊教授 南京师范大学
报告摘要：This paper proposes a novel splitting method for finding a zero point of A+B +C, where A and C are maximal monotone and B is ξ− cocoercive. In designing the algorithm, we utilize the forward step of B in both subproblems, and add “x = y” as a penalty to equilibrate the two subproblems because they have the same accumulation point. We establish the convergence of the proposed method and demonstrate its sublinear convergence rate concerning the fixed-point residuals, assuming mild conditions in an infinite dimensional Hilbert space. This approach not only generalizes the Douglas-Rachford splitting method and the Davis-Yin three-operator splitting method, but also, to our knowledge, uniquely correlates with the symmetric alternating direction method of multipliers (sADMM)-a correspondence absent in current maximal monotone operator splitting algorithms. As an application, we use RSM to solve zero point problems involving multiple operators. By introducing a new space reconstruction method, we transform the problem of multiple operators into a problem of three operators and obtain a distributed version of the RSM. We validate our method’s efficacy through applications to mean-variance optimization, inverse problems in imaging, and the soft-margin support vector machine problem with nonsmooth hinge loss functions, showcasing superior performance against existing algorithms in the literature.
报告人简介：蔡邢菊，南京师范大学教授，博导。主要从事最优化理论与算法、变分不等式、数值优化方向研究工作。主持国家青年基金一项、面上基金一项、省青年基金一项，参加国家重点项目一项，获江苏省科学技术奖一等奖一项。
报告题目三：几类带非光滑项的正交约束优化问题的算法和理论
报告人：姜波教授 南京师范大学
报告摘要: 带非光滑项的正交约束优化问题在人工智能和数据科学等领域中有着广泛的应用。我们将介绍求解几类带非光滑项的正交约束优化问题的高效算法和相关的理论，这些问题包括非负正交约束优化问题、投影鲁棒 Wasserstein 距离和无线通信领域中的大规模阵列天线场景下的一比特编码问题等。
报告人简介: 姜波，南京师范大学数学科学学院教授。2008 年本科毕业于中国石油大学 (华东)，2013 年博士毕业于中国科学院数学与系统科学研究院，2014 年 8 月入职南京师范大学。研究兴趣为: 流形约束优化算法与理论，在 Math. Program., SIAM J. Optim, SIAM J. Sci. Comput., IEEE 汇刊系列等期刊和NeurIPS 2023上发表多篇学术论文。曾入选第三届中国科协青年人才托举工程项目，获得2022年中国运筹学会青年科技奖。
报告题目四：Efficient presolving methods for solving maximal covering and partial set covering location problems
报告人：陈亮 工程师 中国科学院数学与系统科学研究院
报告摘要： The maximal covering location problem (MCLP) and the partial set covering location problem (PSCLP) are two fundamental problems in facility location and have widespread applications in practice. The MCLP determines a subset of facilities to open to maximize the demand of covered customers subject to a budget constraint on the cost of open facilities; and the PSCLP aims to minimize the cost of open facilities while requiring a certain amount of customer demand to be covered. Both problems can be modeled as mixed integer programming (MIP) formulations. Due to the intrinsic NP-hardness nature, however, it is a great challenge to solve them to optimality by MIP solvers, especially for large-scale cases. In this paper, we present five customized presolving methods to enhance the capability of employing MIP solvers in solving the two problems. The five presolving methods are designed to reduce the sizes of the problem formulation and the search tree of the branch-and-cut procedure. For planar problems with an extremely huge number of customers under realistic types of facility coverage, we show that the number of customers in the reduced problems can be bounded above by a quadratic polynomial of the number of facilities. By extensive numerical experiments, the five presolving methods are demonstrated to be effective in accelerating the solution process of solving the MCLP and PSCLP. Moreover, they enable to solve problems with billions of customers, which is at least one order of magnitude larger than those that can be tackled by previous approaches.
报告人简介：陈亮，中国科学院数学与系统科学研究院工程师。2020 年于中国科学院数学与系统科学研究院获得博士学位。是国产混合整数规划软件 CMIP 的创始骨干成员，并持续致力于其研发工作。主要研究方向是混合整数规划算法及其应用。与多家企业合作，重点关注电力调度、供应链、集成电路等领域的混合整数规划问题。获得了中国运筹学会运筹应用奖、北京运筹学会青年优秀论文奖、国家自然科学基金青年科学基金、中国运筹学会青年人才发展专项等，参加了重点研发计划、国家自然科学基金重大项目等，在运筹优化的著名刊物JOGO、EJOR等发表若干文章。
报告题目五：The neural network models for solving absolute value equations
报告人：于冬梅副教授 辽宁工程技术大学
报告摘要: The inverse-free neural network l with mixed delays and inertial inverse-free neural network are proposed to solve the absolute value equations (AVEs). Under mild conditions, the equilibrium points of the dynamical system exist and could be (globally) asymptotically stable. Numerical results illustrate the effectiveness of the presented methods.
报告人简介：于冬梅，博士，辽宁工程技术大学副教授，北京航空航天大学博士后，辽宁省百千万人才工程人选，学校青年教师提升计划—拔尖人才。主持国家自然科学基金青年基金、中国博士后科学基金等多项课题。在《IMA Journal of Numerical Analysis》《Applied Numerical Mathematics》《Optimization》《East Asian Journal on Applied Mathematics》等期刊发表多篇学术论文。
报告题目六：Net-Opt MTL: Variable multi-scale attention fusion network and gradient amending optimization for multi-task learning
报告人： 孟凡云博士 青岛理工大学
报告摘要: Network architecture and optimization are two indispensable parts in multitask learning, which together promote the high performance of multi-task learning. Previous work has rarely focused on both aspects simultaneously. In this paper, we analyze the multi-task learning in scene understanding from network architecture and multi-task optimization. In multi-task network architecture aspect, we propose a variable multi-scale attention fusion network, which overcomes the issue of feature loss when processing small-scale feature maps during upsampling and resolves the problem of inadequate learning in conventional multi-scale models due to significant spatial size disparities. In multi-task optimization aspect, a specific gradient vaccine scheme is put forward to treat the defects of conflicts and dominance of gradients among tasks during the process of multi-task training, and it effectively alleviates the imbalance of multitask training. Various ablation experiments and comparative experiments demonstrate that simultaneously considering the network framework design and multi-task gradient optimization can make great improvement for the performance of multi-task learning.
报告人简介：孟凡云，博士，青岛理工大学信息与控制工程学院计算机科学与技术硕士生导师，2017年分别获得大连理工大学运筹学与控制论博士学位，2023年北京航空航天大学访问学者。主要研究方向为“多任务深度学习”和“多目标优化理论与算法”“图像处理”。主持完成山东省自然科学基金1项。在《Journal of Global Optimization》《Information Sciences》《Set-Valued Variational Analysis》《Optimization》等国际重要期刊发表多篇论文。现任山东省运筹学会理事，美国数学会《数学评论》评论员，中国运筹学会会员，中国工业与应用数学学会会员。
欢迎广大师生踊跃参加！
