Yun-Bin Zhao  (PhD 1998,  CAS)

Senior Lecturer (Associate Professor)

School of Mathematics

University of Birmingham

Edgbaston B15 2TT

Birmingham, UK

Tel:  +44 0121 414 7092

Fax: +44 0121 414 3393




My research interests are in computational optimization, operations research, compressed sensing, numerical analysis, and machine learning.   Following post-doctoral research at the Chinese Academy of Science, Chinese University of Hong Kong and University of Toronto, I was an Assistant Professor and then Associate Professor at the AMSS, Chinese Academy Sciences.  In 2007, I joined onto the University of Birmingham in United Kingdom as a Lecturer and then Senior Lecturer. My research interests include operations researches, computational optimization, sparse optimization, data science, signal processing, compressed sensing, and statistical and machine learning.

Courses taught in 2018/19:   Integer Optimization  (Autumn 2018);    Linear Optimization  (Autumn 2018).   Tutorials for Year 1 and Year 2:   Probability, Statistics, Combinatorics,  Complex Analysis, Multivariable & Vector Analysis, Linear Algebra & Linear Programming.


Office Hours (Autumn 2019):    Thursday 3:45-5:15pm

Editorial Services:

·        Associate Editor:  Applied Mathematics and Computation  (2007--2017)

·       Area Editor:        European Journal of Pure and Applied Mathematics  (2008--)

·       Editorial board:   Journal of Algebraic Statistics  (2010-2014)





1.      Y. B. Zhao,   Sparse Optimization Theory and Methods,  CRC Press, Taylor & Francis Group,  2018.,


Sparse Optimization Theory and Methods   presents the state of the art in theory and algorithms (from optimization perspective) for signal recovery and signal approximation under the sparsity assumption. The up-to-date uniqueness conditions for the sparsest solution of underdertemined linear systems are described. The results for sparse signal recovery under the matrix property called range space property (RSP) are introduced, which is a mild condition for the sparse signal to be recovered by convex optimization methods. This framework is generalized to 1-bit compressed sensing. Two efficient sparsity-seeking algorithms, reweighted l1-minimization in primal space and the algorithm based on complementary slackness property, are presented. The theoretical efficiency of these algorithms is analysed in this book. Under the RSP assumption, the author also provides a unified stability analysis for several popular optimization methods for sparse signal recovery, including l1-mininization, Dantzig selector and LASSO. This book incorporates recent development and author’s latest research in the field that have not appeared in other books.


Publications (selected):


1.      Y.B. Zhao, Optimal k-Thresholding Algorithms for Sparse Optimization Problems, 

SIAM Journal on Optimization,  30 (2020), No. 1, pp. 31-55.

2.      Y.B. Zhao, H. Jiang and Z.-Q. Luo, Weak stability of 1-minimization methods in sparse data reconstruction,

Mathematics of Operations Research,  44 (2019),  no.1,  pp. 173–195.

3.      Y.B. Zhao,  Sparse Optimization Theory and Methods,   CRC Press,  Taylor & Francis Group,  2018.

4.      Y.B. Zhao and Z.-Q. Luo, Constructing new weighted l1-algorithms for the sparsest points of polyhedral sets,

Mathematics of Operations Research,  42 (2017),  no.1, pp. 57--76.

5.      Y.B. Zhao and C. Xu,  1-bit compressive sensing: Reformulation and RRSP-based sign recovery theory,

Science China Mathematics, 59 (2016),  No. 10,  pp. 2049–2074. 

6.      Y.B. Zhao and M. Kocvara, A new computational method for the sparsest solutions to systems of linear equations,

SIAM Journal on Optimization,  25 (2015), No. 2, pp. 1110–1134.

7.      Y.B. Zhao, Equivalence and strong equivalence between the sparsest and least $ \ell_1$-norm nonnegative solutions of linear systems and their applications. 

J. Oper. Res. Soc. China, 2 (2014),  no. 2,  pp. 171–193. (PDF)

8.      Y.B. Zhao, RSP-Based analysis for sparest and least $\ell_1$-norm solutions to underdetermined linear systems,  

IEEE Transactions on Signal Processing,  61 (2013),  no. 22, pp. 5777-5788.  DOI:  10.1109/TSP.2013.2281030

9.      Y.B. Zhao and D. Li,  Reweighted $\ell_1$-minimization for sparse solutions to underdetermined linear systems,

SIAM Journal on Optimization, 22 (2012), No. 3,  pp. 1065-1088.

10.  Y.B. Zhao,  An approximation theory of matrix rank minimization and its application to quadratic equations,   

Linear Algebra and its Applications, 437 (2012),  pp.77-93.

11.  Y.B. Zhao,  The Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms,

SIAM Journal on Matrix Analysis & Applications, 31 (2010), no.4, pp.1792-1811.

12.  I. Averbakh and Y.B. Zhao,  Explicit reformulations for robust optimization problems with general uncertainty sets

SIAM Journal on Optimization, 18 (2008), pp. 1436-1466

13.  Y.B. Zhao,  S.C. Fang and  D. Li, Constructing generalized mean functions via convex functions with   regularity  conditions,  

SIAM Journal on Optimization , 17  (2006) ,  pp. 37-51. 

14.  J. Peng,  T. Terlaky and Y.B. Zhao, An interior point algorithm for linear optimization based on a  proximity  function, 

SIAM Journal on Optimization,   15(2005),    pp. 1105-1127.

15.  Y.B. Zhao and  D. Li,   A  globally  and  locally  convergent  non- interior- point algorithm for   P_0 LCPs, 

SIAM Journal on Optimization,  13 (2003), no.4, 1195—1221. 

16.  Y.B. Zhao and  D. Li,   Locating the least 2-norm solution of linear programming  via the  path- following methods,  

SIAM Journal on Optimization.  12 (2002), no. 4, 893--912. 

17.  Y.B. Zhao and D. Li,   Exitstence and limiting behavior of a non-interior-point trajectory for CPs without strict feasibility condition

SIAM Journal on Control and Optimization. 40 (2001), pp. 898-924. 

18.  Y.B. Zhao and D. Li,   Monotonicity of fixed point and normal mappings associated with variational inequality and its application.  

SIAM Journal on Optimization,   11 (2001),  no 4,  pp. 962-973.

19.  Y.B. Zhao and D. Li,  On a new  homotopy  continuation  trajectory  for  nonlinear  complementarity  problems,  

Mathematics of Operations Research,  26 (2001),  no. 1  pp. 119-146.

20.  Y.B. Zhao and  G. IsacProperties of a multi-valued mapping associated with some non-monotone complementarity problems,  

SIAM Journal on Control and Optimization. 39 (2000), pp. 571-593. 


 Full list of publications (1995-2020)  can be found here.   


 Recent Presentations:


1.   Data (Signal) Reconstruction Algorithms: New stability theory”, 2017/2018

2.   Dual density-based reweighted l1-algorithms for sparse optimization problem”, 2016/2017

3.    Efficiency of l1-minimization for l0-minimization problems: Analysis via the Range Space Property”,  2013/2014.

4.   Locating sparse solutions of underdetermined linear system via the reweighted l1-method”, 2012.