Yun-Bin Zhao (PhD 1998, CAS)
Senior Lecturer in Mathematical Optimization
University of Birmingham
Edgbaston B15 2TT
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 ℓ1-minimization methods in sparse data reconstruction,
Mathematics of Operations Research, Published online in Articles in Advance 14 Sep 2018, https://doi.org/10.1287/moor.2017.0919
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)
IEEE Transactions on Signal Processing, 61 (2013), no. 22, pp. 5777-5788.
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.
Linear Algebra and its Applications, 437 (2012), pp.77-93.
Applied Mathematics and Optimization, 62 (2010), no. 3, pp. 411-434.
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.
SIAM Journal on Control and Optimization. 40 (2001), pp. 898-924.
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. Isac, Properties of a multi-valued mapping associated with some non-monotone complementarity problems,
SIAM Journal on Control and Optimization. 39 (2000), pp. 571-593.