| Abstract | Semidefinite Programming (SDP) has been a major research topic in optimization during the last three decades due to its mathematical elegance as well as its rich applications in many fields. It is widely believed that interior point methods (IPMs) are perhaps the most robust and efficient algorithms for solving small to medium sized SDP problems. For large scale SDPs, IPMs are no longer viable due to their inherent high memory requirements and computational costs at each iteration. In this talk, we will summarize what we have done during the last 20 years or so in combining the augmented Lagrangian algorithm with the semismooth Newton method for solving the dual of SDP and convex quadratic SDP of large scales. We will emphasize the importance of the constraint non-degeneracy in numerical implementations and the quadratic growth condition in convergence rate analysis. Easy-to-implement stopping criteria for the augmented Lagrangian subproblems will also be introduced. All these features are implemented in the publically available software packages SDPNAl/SDPNAL+ and QSDPNAL. |
| Affiliation | Professor Defeng Sun is currently Chair Professor of Applied Optimization and Operations Research at the Hong Kong Polytechnic University. He mainly publishes in non-convex continuous optimization and machine learning. Together with Professor Kim-Chuan Toh and Dr Liuqin Yang, he was awarded the triennial 2018 Beale--Orchard-Hays Prize for Excellence in Computational Mathematical Programming by the Mathematical Optimization Society. He served as editor-in-chief of Asia-Pacific Journal of Operational Research from 2011 to 2013 and he now serves as associate editor of Mathematical Programming, SIAM Journal on Optimization, Journal of the Operations Research Society of China, Journal of Computational Mathematics, and Science China: Mathematics. In 2020, he was elected as a Fellow of the societies SIAM and CSIAM. |
