Welcome to my homepage

News

• [December 18, 2025] New preprint "Facial reduction for nice (and non-nice) convex programs".

• [November 27, 2025] New preprint "A nonmonotone extrapolated proximal gradient-subgradient algorithm beyond global Lipschitz gradient continuity".

• [April 25, 2025] New preprint "On the equivalence of a Hessian-free inequality and Lipschitz continuous Hessian".    

Background

I received my Bachelor degree in July 2010 from Wuhan University, School of Mathematics and Statistics. I got my PhD degree in Computational Mathematics in July 2015 from  Chinese Academy of Sciences, Academy of Mathematics and Systems Science, under the supervision of Professor Yu-Hong Dai. I was  a Postdoctoral Fellow in Department of Applied Mathematics at The Hong Kong Polytechnic University from March 2016 to August 2018, under the mentorship of Professor Ting Kei Pong. I was a Postdoctoral Researcher from September 2018 to March 2021 in RIKEN AIP Center hosted by Professor Akiko Takeda. I was an assistant professor at Tokyo Institute of Technology from April 2021 to April 2025. I am currently an associate professor at  University of Tsukuba.

This is my CV.

Research Interests

Nonconvex optimization: algorithm and analysis

Preprints 

1. Ying Lin, Tianxiang Liu and Bruno F. Lourenço. Facial reduction for nice (and non-nice) convex programs. 

2. Lei Yang, Jingjing Hu and Tianxiang Liu. A nonmonotone extrapolated proximal gradient-subgradient algorithm beyond global Lipschitz gradient continuity.   

3. Radu I. Boţ, Minh N. Dao, Tianxiang Liu, Bruno F. Lourenço and Naoki Marumo. On the equivalence of a Hessian-free inequality and Lipschitz continuous Hessian.

4. Tianxiang Liu and Bruno F. Lourenço. Concrete convergence rates for common fixed point problems under Karamata regularity. 

Publications

1. Charles Namchaisiri, Tianxiang Liu and Makoto Yamashita. A new dual spectral projected gradient method for log-determinant semidefinite programming with hidden clustering structures.  Comput. Optim. Appl. 92, pp. 589-615, 2025.92, pages 589–615 92, pages 589–615

2. Tianxiang Liu and Bruno F. Lourenço. Convergence analysis under consistent error bounds.  Found. Comput. Math. 24, pp. 429-479, 2024.

3.  Tianxiang Liu, Ting Kei Pong and Akiko Takeda. Doubly majorized algorithm for sparsity-inducing optimization problems with regularizer-compatible constraints. Comput. Optim. Appl. 86,  pp. 521-553, 2023. [code]

4. Tianxiang Liu and Akiko Takeda. An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems. Comput. Optim. Appl. 82,  pp. 141-173, 2022. [code] 

5. Tianxiang Liu, Ivan Markovsky, Ting Kei Pong and Akiko Takeda. A hybrid penalty method for a class of optimization problems with multiple rank constraints. SIAM J. Matrix Anal. A. 41, pp. 1260-1283, 2020. [code]

6. Ivan Markovsky, Tianxiang Liu and Akiko Takeda. Data-driven structured noise filtering via common dynamics estimation.  IEEE Trans. Signal Process, 68,  pp. 3064-3073, 2020.

7. Tianxiang Liu, Zhaosong Lu, Xiaojun Chen and Yu-Hong Dai. An exact penalty method for semidefinite-box constrained low-rank matrix optimization problems. IMA J. Numer. Anal. 40, pp. 563-586, 2020.

8. Tianxiang Liu, Ting Kei Pong and Akiko Takeda. A refined convergence analysis of pDCAe with applications to simultaneous sparse recovery and outlier detection. Comput. Optim. Appl. 73,  pp. 69-100, 2019.

9. Tianxiang Liu, Ting Kei Pong and Akiko Takeda. A successive difference-of-convex approximation method for a class of nonconvex nonsmooth optimization problems. Math. Program. 176,  pp. 339–367, 2019.  

10. Guoyin Li, Tianxiang Liu and Ting Kei Pong. Peaceman-Rachford splitting for a class of nonconvex optimization problems.  Comput. Optim. Appl. 68, pp. 407-436, 2017. 

11. Tianxiang Liu and Ting Kei Pong. Further properties of the forward-backward envelope with applications to difference-of-convex programming. Comput. Optim. Appl. 67, pp. 489-520, 2017.

Talks

1. RAMP2023. エラーバウンド, 正則変動及び明示的な収束率 , 東京, 2023年11月20-21日.

2. 日本OR学会2021年秋季研究発表会. DC問題に対する非厳密Newton型近接勾配法, 東京 (zoom), 2021年９月16日-17日.

3. OP21. Convergence analysis under consistent error bounds, Online (zoom), July 20-23, 2021.

4. 日本OR学会2021年春季研究発表会. 穏当なエラーバウンドと収束解析, 東京 (zoom), 2021年３月2日-3日.

5. ICCOPT2019. A successive difference-of-convex approximation method with applications to control problems, Berlin, August 3-8, 2019. 

6. EURO2018. A successive difference-of-convex approximation method for a class of nonconvex nonsmooth optimization problems, Valencia, July 8-11, 2018.

7. ISMP2018. A successive difference-of-convex approximation method for a class of nonconvex nonsmooth optimization problems, Bordeaux, July 1-6, 2018.

8. SIAM-ALA18. An exact penalty method for semidefinite-box constrained low-rank matrix optimization problems, Hong Kong, May 4-8, 2018.

9. OP17. Further properties of the forward-backward envelope with applications to difference-of-convex programming, Vancouver, May 22-25, 2017.

Visits

1. June 2014 - June 2015, The Hong Kong Polytechnic University, hosted by Professor Xiaojun Chen.

Links

My link in Google Scholar.