welcome to homepage of Dr Yunbin Zhao

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)

Monograph:

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

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. https://doi.org/10.1137/18M1219187

2. Y.B. Zhao, H. Jiang and Z.-Q. Luo, Weak stability of ℓ1-minimization methods in sparse data reconstruction,

Mathematics of Operations Research, 44 (2019), no.1, pp. 173–195. https://doi.org/10.1287/moor.2017.0919

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

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. https://doi.org/10.1287/moor.2016.0791

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. https://doi.org/10.1137/140968240

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,