Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	梁令博士，威尔斯特拉斯应用与分析研究所
Inviter:
Title:	A Squared Smoothing Newton Method for Semidefinite Programming
Language:	Chinese
Time & Venue:	2023.03.27 15:30-17:00 腾讯会议: 803-304-619
Abstract:	This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber function. Using these results and existing ones in the literature, we then conduct rigorous convergence analysis and establish convergence properties for the proposed algorithm. In particular, we show that the proposed method is well-defined and admits global convergence. Moreover, under suitable regularity conditions, i.e., the primal and dual constraint nondegenerate conditions, the proposed method is shown to have a superlinear convergence rate. To evaluate the practical performance of the algorithm, we conduct extensive numerical experiments for solving various classes of SDPs. Comparison with the state-of-the-art SDP solver SDPNAL+ demonstrates that our method is also efficient for computing accurate solutions of SDPs.