报告一题目：Optimization, feasibility, bounded perturbation resilience, superiorization and applications

报告时间：2023年9月23日（周六）9:00-10:00

报告地点：学术交流中心十二会议室

主讲人：Aviv Gibali

摘要：In this talk we'll overview some results related to the convex feasibility and related optimization models for various applications. Moreover, we'll present the superiorization and the bounded perturbation resilience of algorithms and show how such methodology can be used to speed-up convergence of given algorithm as well as help for treating non-convex objective functions.

报告二题目：Convex and Non-Convex Impulse Noise Image Restoration Model and Algorithm

报告时间：2023年9月23日（周六）10:00-11:00

报告地点：学术交流中心十二会议室

主讲人：唐玉超

摘要：Image restoration with impulse noise is an important task in image processing. Although there are many effective methods for removing impulse noise in image restoration, there is still much room for improvement. In this talk, we will discuss our two recent works: (i) First, we propose a new two-phase method for solving such a problem, which combines the nuclear norm and the total variation regularization with box constraint. The popular alternating direction method of multipliers and the proximal alternating direction method of multipliers are employed to solve this problem. (ii) Second, we propose an efficient iterative algorithm to solve nonconvex models arising in impulse noise. Compared to existing algorithms, our proposed algorithm is a completely explicit algorithm in which every subproblem has a closed-form solution. The key idea is to transform the original nonconvex models into an equivalent constrained minimization problem with two separable objective functions, where one is differentiable but nonconvex. Numerical experiments demonstrate that the proposed method performs better than the state-of-the-art methods in terms of both subjective and objective evaluations.

报告三题目：The Generalized Modular String Averaging Procedure

报告时间：2023年9月23日（周六）13:30-14:30

报告地点：学术交流中心十二会议室

主讲人：Aviv Gibali

摘要：A modular string averaging (MSA) procedure provides a flexible algorithmic framework for solving various feasibility problems such as common fixed point and convex feasibility problems.

In this talk we'll introduce an extension of the MSA procedure to an infinite sequence of operators with admissible controls. Various applications of these concepts are presented with respect to weak and strong convergence.

报告人简介

1. Aviv Gibali is an Associate Professor and the Head of the Mathematics Department at the Braude College of Engineering (Israel). He obtained his Bachelor Degree in Mathematics at the University of Haifa in Israel (2005) and his PhD at The Technion – Israel Institute of Technology (2012) with a PhD thesis devoted to the development of algorithms for solving variational inequalities and its applications. Aviv is an algorithm designer in the field of Optimization with application to image processing, radiation therapy and more. He serves as Associate Editor for several high-ranked journals in the field such as Journal of Optimization Theory and Applications, Numerical Algorithms, Applied Numerical Mathematics and Fixed Point Theory and Algorithms for Sciences and Engineering. He published more than 90 scientific papers with publications with 4038 citations and H-index of 28.

2. 唐玉超：广州大学教授，博士生导师。2013年西安交通大学数学与统计学院博士毕业。主要研究方向图像处理中的优化模型和算法。在研国家自然科学基金地区项目1项，主持完成国家自然科学基金地区项目、国家自然科学基金青年项目、江西省自然科学基金青年项目和江西省教育厅青年科学基金项目各1项。已在《Inverse Problems and Imaging》、《中国科学数学》、《Journal of Computational Mathematics》、《Applied Mathematics Letters》、《Mathematical and Computer Modelling》、《Nonlinear Analysis: Theory, Methods & Applications 》和《Numerical Algorithms》等国内外期刊发表论文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。