报告题目：A proximal algorithm with backtracked extrapolation for a class of structured fractional programming
报告人： 张娜副教授，华南农业大学
报告时间：2022年5月26日上午10：30-11：30
报告地点：龙洞行政楼610
主持人： 林荣荣

报告摘要：We consider a class of structured fractional minimization problems where the numerator part of the objective is the sum of a convex function and a Lipschitz differentiable (possibly) nonconvex function, while the denominator part is a convex function. By exploiting the structure of the problem, we propose a first-order algorithm, namely, a proximal-gradient-subgradient algorithm with backtracked extrapolation (PGSA_BE) for solving this type of optimization problem. It is worth pointing out that there are a few differences between our backtracked extrapolation and other popular extrapolations used in convex and nonconvex optimization. One of such differences is as follows: if the new iterate obtained from the extrapolated iteration satisfies a backtracking condition, then this new iterate will be replaced by the one generated from the non-extrapolated iteration. We show that any accumulation point of the sequence generated by PGSA_BE is a critical point of the problem regarded. In addition, by assuming that some auxiliary functions satisfy the Kurdyka-Łojasiewicz property, we are able to establish global convergence of the entire sequence, in the case where the denominator is locally Lipschitz differentiable, or its conjugate satisfies the calmness condition. Finally, we present some preliminary numerical results to illustrate the efficiency of PGSA_BE.

专家简介：张娜，华南农业大学数学与信息学院副教授，硕士生导师。研究领域包括最优化理论及算法、信号及图像处理。论文发表在SIAM Journal on Optimization, Applied and Computational Harmonic Analysis, Inverse Problems等国际知名期刊。2017 年论文入选《Inverse Problems》Highlight论文，获得2015年中国计算数学年会优秀青年论文竞赛一等奖，获得2021年广东省计算数学学会优秀青年学术成果一等奖。主持国家自然科学基金两项（青年和天元专项基金青年），广东省自然科学基金一项等多项科研项目。