題  目：Landscape analysis of non-convex optimizations in phase retrieval

内容簡介：Non-convex optimization is a ubiquitous tool in scientific and engineering research. For many important problems, simple non-convex optimization algorithms often provide good solutions efficiently and effectively, despite possible local minima. One way to explain the success of these algorithms is through the global landscape analysis. In this talk, we present some results along with this direction for phase retrieval. The main results are, for several of non-convex optimizations in phase retrieval, a local minimum is also global and all other critical points have a negative directional curvature. The results not only will explain why simple non-convex algorithms usually find a global minimizer for phase retrieval, but also will be useful for developing new efficient algorithms with a theoretical guarantee by applying algorithms that are guaranteed to find a local minimum.

報告人：蔡劍鋒

報告人簡介：香港科技大學數學系教授，主要研究興趣為信号，圖像和數據的理論和算法基礎。他在矩陣恢複，圖像重構和成像算法等領域，取得了一系列開創性的科研成果。其關于矩陣補全的SVT算法對學術研究和實際應用産生重要影響，該文章谷歌被引次數超6000次。蔡劍鋒教授關于圖像重構的工作發表于被譽為數學四大期刊之一的Journal of the AMS。蔡劍鋒教授在2017年和2018年被評為全球高被引學者，學術文章總被引超13000次。

時  間：2024年1月3日（周三）上午8：00 開始

地  點：南海樓124室

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