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    Department of Systems Engineering and Engineering Management

                       The Chinese University of Hong Kong

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Date: Friday, January 26, 4:30 pm – 5:30 pm

Venue: ERB 513, The Chinese University of Hong Kong

Title:An efficient sieving based secant method for sparse optimization problems with least-squares constraints

Speaker: Prof. Yancheng Yuan, Hong Kong Polytechnic University

Abstract:

We propose an efficient sieving based secant method to address the computational challenges of solving sparse optimization problems with least-squares constraints. A level-set method has been introduced in [X. Li, D.F. Sun, and K.-C. Toh, SIAM J. Optim., 28 (2018), pp. 1842--1866] that solves these problems by using the bisection method to find a root of a univariate nonsmooth equation φ(λ)=ϱ for some ϱ>0, where φ(⋅) is the value function computed by a solution of the corresponding regularized least-squares optimization problem.  When the objective function in the constrained problem is a polyhedral gauge function, we prove that (i) for any positive integer k, φ(⋅) is piecewise C^k in an open interval containing the solution λ^* to the equation φ(λ)=ϱ; (ii) the Clarke Jacobian of φ(⋅) is always positive. These results allow us to establish the essential ingredients of the fast convergence rates of the secant method. Moreover, an adaptive sieving technique is incorporated into the secant method to effectively reduce the dimension of the level-set subproblems for computing the value of φ(⋅). The high efficiency of the proposed algorithm is demonstrated by extensive numerical results.
This is a joint work with Qian Li and Defeng Sun.

Biography:

Yancheng Yuan is an assistant professor in the Department of Applied Mathematics at the Hong Kong Polytechnic University. His primary research interests lie in the theoretical and applied aspects of continuous optimization and machine learning. He has published papers in prestigious journals such as the "SIAM Journal on Optimization," "Journal of Machine Learning Research," and "IEEE Transactions on Neural Networks and Learning Systems", as well as presented at top academic conferences in the field of machine learning such as ICML, NeurIPS, and WWW. He has received the Best Paper Award Finalist (WWW 2021).

Everyone is welcome to attend the talk!

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