CIAO Seminar: Prof. Hong Kun Xu, Projection methods for constrained minimization of a finite sum of convex functions

Speaker: Prof. Hong Kun Xu
Hangzhou Dianzi University

Time and Location: Thursday, August 10 at 11:30 AM – 12:30 PM, T121, Mount Helen Campus

Title: Projection methods for constrained minimization of a finite sum of convex functions.

Abstract: Projection methods are introduced to minimize a finite sum of convex functions over the intersection finitely many closed convex subsets of a Hilbert space. These algorithms consist of two steps. The first step is an inner circle of gradient descent process to be executed through each component function and the second step is projection process (e.g., sequential or parallel or cyclic projection) that is applied to produce the next iterate. These algorithms are proved in the finite-dimensional case to converge to an optimal solution of the full minimization problem by assuming boundedness of the gradients at the iterates of the component functions and the stepsizes being chosen appropriately. Weak convergence in the infinite-dimensional case will also be investigated. Some open questions will be raised.

Bio: Prof Hong Kun Xu is currently distinguished professor at Hangzhou Dianzi University. In 2014 he was selected by the Zhejiang “1000 Talents” program. He has addressed many international conferences as invited and keynote speaker. Xu is a winner of several awards, including the 2004 South African Mathematical Society Research Distinction. He was elected fellow to the Academy of Science of South Africa in 2005 and to TWAS, the World Academy of Sciences, in 2012. He has been Thomson Reuters Highly Cited Researcher since 2013.

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