Title: Exploring the Data and Solution Sparsity in Sparse Statistical Optimization Problems

Time: 2020-11-05  20:00 - 21:00

Speaker: Prof.Defeng Sun   The Hong Kong Polytechnic University

Venue: Tencent Meeting    ID:225 762 445

Abstract: It is widely believed by many researchers, in particular by those outside the traditional optimization community, that the second-order methods such as Newton’s method are no longer applicable for solving large scale optimization problems. This is partially true for optimization models that neither need a good optimal solution nor need to be solved quickly. In this talk, we shall first use large scale statistical optimization problems arising from machine learning to explain why the second-order methods, in particular the proximal point dual Newton methods (PPDNA), if wisely used, can be much faster than the first-order methods. The key point is to make use of the second order sparsity of the optimal solutions in addition to the data sparsity so that, at each iteration, the computational costs of the second order methods can be comparable or even lower than those of the first order methods. Equipped with the PPDNA, we shall then introduce adaptive dimension-reduction methodologies to generate solution paths of very large sparse statistical optimization problems of particular importance in applications. Finally, we shall illustrate the high efficiency of our approach with extensive numerical results.