Xiantao Xiao received his Ph. D. degree supervised by Prof. Liwei Zhang in operations research from Dalian University of Technology in 2009. He is currently an Associate Professor in School of Mathematical Sciences at Dalian University of Technology. His research interest is in the area of mathematical optimization, currently focuses on the algorithms of structural convex programs, stochastic methods based on stochastic approximation.

Google Scholar

ResearchGate

Selected Research Results

(1) Second-order Algorithms for Composite Optimization 

Composite optimization problems arise frequently from the area of machine learning, signal processing and statistics. Many popular first-order algorithms are proposed in recent years. However, these algorithms always converge slowly especially in the neighborhood of optimal solutions. Due to the nonsmooth structure of the problems, second-order algorithms are difficult to propose. We propose a semismooth Newton method equipped with regularized projection step, and lately extend it to solve stochastic composite optimization.

Selected related papers

1. X. Xiao, Y. Li, Z. Wen, L. Zhang. A regularized semi-smooth Newton method with projection steps for composite convex programs. Journal of Scientific Computing, 2018, 76(1), 364-389

2. A. Milzarek, X. Xiao, S. Cen, Z. Wen, M. Ulbrich. A stochastic semismooth Newton method for nonsmooth nonconvex optimization. SIAM Journal on Optimization, 2019, 29(4), 2916-2948

3. A. Milzarek, X. Xiao, Z. Wen, M. Ulbrich. On the local convergence of a stochastic semismooth Newton method for nonsmooth nonconvex optimization. SCIENCE CHINA Mathematics, accepted

(2) Stochastic Approximation Algorithms for Expectation Constrained Stochastic Programming

Stochastic programming with expectation functional constraints (SPEC) are standard in the field of stochastic optimization. However, efficiently algorithms for solving  SPEC are limited. We firstly propose a penalized stochastic approximation algorithms, and establish the almost surely global convergence and expected convergence rates. Then,  we study a type of stochastic augmented Lagrangian method, namely stochastic proximal methods of multipliers (SPMM), to solve SPEC. To handle the subproblems of SPMM, we also propose a class of model-based SPMM, in which the corresponding subproblems can be efficiently solved by propely selecting the model.

Selected related papers

1. X. Xiao. Penalized stochastic gradient methods for stochastic convex optimization with expectation constraints. Optimization-online

2. L. Zhang, Y. Zhang, X. Xiao, J. Wu. Stochastic Approximation Proximal Method of Multipliers for Convex Stochastic Programming. Mathematics of Operations Research, accepted

3. L. Zhang, Y. Zhang, J. Wu, X. Xiao. A stochastic linearized proximal method of multipliers for convex stochastic optimization with expectation constraints. https://arxiv.org/pdf/2106.11577

(3) Smoothing Methods for Chance Constrained Programs

Chance constraint is one of the most popular techniques to deal with uncertainty in optimization. Due to the nonsmoothness and nonconvexity of chance constraint, it is usually difficult to solve chance constrained programs (CCP). We propose a smoothing framework to approximation CCP with  smooth nonconvex programs and apply a sequential convex program method to solve them. By using variational analysis, we establish the relations of optimization sets between CCP and the corresponding smooth programs.

Selected related papers

1. F. Shan, L. Zhang, X. Xiao. A smoothing function approach to joint chance-constrained programs. Journal of Optimization Theory and Applications, 2014, 163(1), 181-199

2. F. Shan, X. Xiao, L. Zhang. Convergence analysis on a smoothing approach to joint chance constrained programs. Optimization, 2016, 65(12), 2171-2193