** **

** Yun-Bin Zhao (**PhD
1998, CAS)

Senior Lecturer in Mathematical Optimization

University of Birmingham

Edgbaston B15 2TT

Birmingham, UK

Tel: +44 0121 414
7092

Fax: +44 0121 414 3393

Email: y.Zhao.2@bham.ac.uk

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)

**Monograph: **

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)

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. 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.

**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.