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Landscape Analysis of Non-Convex Optimizations in Phase Retrieval

Dc5a76e28ded541eedefc59ce4ee26cb51a24617

Speaker

Jianfeng Cai, Hong Kong University of Science and Technology

Time

2020.07.15 14:00-15:00

Venue

Online—ZOOM APP

ZOOM Info

ZOOM Link

Conference ID: 941-874-50523

PIN Code: 689626

Abstract

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.

Slides

Landscape Analysis of Non-Convex Optimizations in Phase Retrieval

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