Department of Mathematics

Applied Mathematics

  •  Jianfeng Cai, Hong Kong University of Science and Technology
  •  Landscape analysis of non-convex optimizations in phase retrieval
  •  03/11/2021
  •  3:30 AM - 4:30 AM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Olga Turanova (turanova@msu.edu)

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 explain why simple non-convex algorithms usually find a global minimizer for phase retrieval, but also are useful for developing new efficient algorithms with a theoretical guarantee by applying algorithms that are guaranteed to find a local minimum.

 

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