Nonconvex Geometry of Low-Rank Optimizations

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• Dr Gongguo Tang, Colorado School of Mines
• Thursday 04 May 2017, 11:00-12:00
• Room 611 (Gabor Seminar Room), EEE Building.

If you have a question about this talk, please contact Wei Dai.

Abstract: The past few years have seen a surge of interest in nonconvex reformulations of convex optimizations using nonlinear reparameterizations of the optimization variables. Compared with the convex formulations, the nonconvex ones typically involve many fewer variables, allowing them to scale to scenarios with millions of variables. However, one pays the price of solving nonconvex optimizations to global optimality, which is generally believed to be impossible. In this talk, I will characterize the nonconvex geometries of several low-rank matrix optimizations. In particular, I will argue that under reasonable assumptions, each critical point of the nonconvex problems either corresponds to the global optimum of the original convex optimizations, or is a strict saddle point where the Hessian matrix has a negative eigenvalue. Such a geometric structure ensures that many local search algorithms can converge to the global optimum with random initializations. Our analysis is based on studying how the convex geometries are transformed under nonlinear parameterizations.

Bio: Dr. Gongguo Tang is an Assistant Professor in the Electrical Engineering and Computer Science Department at Colorado School of Mines (CSM) since 2014. He received his Ph.D. degree in Electrical Engineering from Washington University in St. Louis in 2011. He was a Postdoctoral Research Associate at the Department of Electrical and Computer Engineering, University of Wisconsin-Madison from 2011 to 2013, and a visiting scholar at the University of California, Berkeley in 2013. Dr. Tang’s research interests are in the area of signal processing, convex optimization, machine learning, and their applications in big data analytics, optics, imaging, and networks. He is a recipient of CSM ’s Junior Faculty Research Award (2016) and AFOSR ’s Summer Faculty Fellowship (2015).

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