Yun-Bin Zhao  (PhD 1998,  CAS)

Senior Lecturer in Mathematical Optimization

School of Mathematics

University of Birmingham

Edgbaston B15 2TT

Birmingham, UK

Tel:  +44 0121 414 7092

Fax: +44 0121 414 3393




Yunbin Zhao received his PhD in Operations Research in 1998 from the Chinese Academy of Sciences. Before joining the University of Birmingham in 2007,   he had worked at the Academy of Mathematics and System Science (AMSS), Chinese Academy of Sciences, Beijing,  the  SEEM of  Chinese University of Hong Kong  and the Management Department of University of Toronto (Canada).     His interest covers computational optimization, operations research and numerical analysis.  Recently, he is working on theory and algorithms for the sparsest solution of linear systems and their applications to compressed sensing,  sparse signal and imaging processing.

Courses  taught  in 2014/15:      Integer Optimization  (Autumn 2014);    Linear Optimization  (Spring 2015);       

Office Hours (Spring 2018):    Thursday 10:00-11:30am

Research Project:       Foundation and reweighted algorithms …with application to data processing (2013-2015)

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)

·        Co-Guest Editor of Journal of Industrial Management and Optimization (Vol. 2 & 3,  2005)

·        Guest Editor of  Journal of Industrial Management and Optimization (2010/2011)





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 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.


Journal articles (selected):


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

Mathematics of Operations Research,   Published online in Articles in Advance 14 Sep 2018,

2.      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.

3.      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. 

4.      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.

5.      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)

6.      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.

7.      Y.B. Zhao, New and improved conditions for uniqueness of sparsest solutions of underdetermined linear systems, 

Applied Mathematics and Computation, 224 (2013), pp. 58-73.

8.      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.

9.      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.

10.   Y.B. Zhao,  The convexity condition and Legendre-Fenchel transform of the product of finitely many quadratic forms,

Applied Mathematics and Optimization, 62 (2010),  no. 3,  pp. 411-434.

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 (1995-2017)  can be found here.   


 Recent Presentations:


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

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