A globally convergent regularized Newton method for l_q-norm composite optimization problems

报告题目A globally convergent regularized Newton method for l_q-norm composite optimization problems

报告专家:Yang Xiaoqi (Hong Kong Polytechnic University)




In this talk we will discuss the composite optimization problem with a twice continuously differentiable loss function and an l_q-norm regularized term. For this class of nonconvex and nonsmooth composite problems, we will review some existing first-order and second-order algorithms. In this work, we propose a hybrid of proximal gradient method and subspace regularized Newton method. The whole iterate sequence produced by the algorithm is proved to have a finite length and converge to an L-type stationary point under a mild curve-ratio condition and the Kurdyka-Lojasiewicz property of the cost function, which converges linearly if further a Kurdyka-Lojasiewicz property of exponent 1/2 holds. Moreover, a superlinear convergence rate for the iterate sequence is also achieved under an additional local error bound condition. Our convergence results do not require the isolatedness and strict local minimality properties of the L-stationary point. Numerical comparisons with some existing algorithms for the l_q-norm regularized linear and logistic regressions on real data indicate that our algorithm not only requires much less computing time but also yields comparable even better sparsities and objective function values.


Xiaoqi Yang received his BSc in Mathematics from Chongqing Jianzhu University in 1982, MSc in Operations Research and Optimal Control from Chinese Academy of Science in 1987, his PhD from The University of New South Wales in 1994. He joined Department of Applied Mathematics, The Hong Kong Polytechnic University in 1999 as an Assistant Professor and then an Associate Professor 2005, and now is a Professor since 2006. His research interests include variational analysis, stability theory, vector optimization and financial optimization. He is a co-author of three research monographs, has over 250 publications and a co-editor of three edited books. He is the recipient of ISI Citation Classic 2000 and an associate editor for several international journals, including Journal of Optimization Theory and Applications. He publishes papers in high-quality journals, such as Management Science, Operations Research, Mathematical Programming, SIAM Journal on Optimization. He was a plenary speaker in Annual Meeting of Chinese Society of Operations Research, in 2014. He has been awarded The President Award for Outstanding Performance/Achievement - Research and Scholarly Activities in The Hong Kong Polytechnic University in 2000 and 2017.