报告人：蔡剑锋教授

             香港科技大学

题目：Favourable Landscape of Phase Retrieval Problem with Optimal Sampling Complexity

时间：2018年07月04日下午15:00

地点：海韵实验楼105

摘要：There are many efficient numerical solvers based on non-convex optimizations for the phase retrieval problem. Despite possible local minima of nonconvex objective functions, these algorithms often work remarkably well to find the global minimum. To explain this phenomenon theoretically, there are two frameworks. One theoretical framework is based on the analysis of the nonconvex objective functions locally in a small neighbourhood of global minimizers. It first constructs a special initialization that is close enough to a global minimizer, and then proves convergence of nonconvex algorithms to the global minimizer. This explanation usually needs only O(n) samples, the optimal sampling complexity. However, it does not explain why nonconvex algorithm with arbitrary initializations still works well. The other theoretical framework analyzes the nonconvex optimization more globally. It proves that nonconvex objective functions in phase retrieval have a favourable landscape - any local minimum is global. Therefore, it is not an issue to get trapped into a local minimum. To have such a favourable landscape, the best existing result needs O(n log^3n) samples, which is not optimal. In this talk, the speaker proves that, with O(n) samples, some nonconvex objective functions for phase retrieval can still have the favourable landscape.

报告人简介：蔡剑锋分别于复旦大学和香港中文大学获得学士和博士学位，先后在新加坡国立大学、美国加州大学洛杉矶分校和爱荷华大学任职博士后、访问助理教授、助理教授等，目前是香港科技大学数学系副教授。他的研究兴趣是成像科学和数据科学中的数学方法，包括数值线性代数、优化、计算调和分析、逼近论和概率，已在J. Amer. Math. Soc.、 Appl. Comput. Harmon. Anal.、SIAM J. Optim.、SIAM J. Sci. Comput.、Math. Comp.、Numer. Math.等数学一流期刊发表论文40余篇。蔡剑锋是2017年全球高引用科学家之一。

联系人：杜魁教授

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