I am currently (2021–) an ARC Discovery Early Career Research Fellow, and was (2016–2020) a Lecturer, in the Department of Electrical and Computer Systems Engineering at Monash University in Melbourne, Australia. In June 2015 I completed my PhD in EECS at MIT where I was part of the Laboratory for Information and Decision Systems (LIDS). From June 2015-June 2016 I was a Research Associate (postdoc) at the University of Washington and a Postdoctoral Scholar at Caltech. |

Email:

Office: Room 221, 14 Alliance Lane (Building 72), Monash University (Clayton)

Phone: +61 3 9905 3500

I am currently looking for PhD students who are interested in doing foundational research in mathematical optimisation and its applications. If you have a strong mathematical background, and an interest in developing and analysing new computational methods, with performance guarantees, for problems in areas such as signal processing, statistics, and machine learning, please contact me.

J. Saunderson,

*A convex form that is not a sum of squares*, May 2021. [arxiv] [YouTube]B. F. LourenĂ§o, V. Roshchina, J. Saunderson,

*Hyperbolicity cones are amenable*, February 2021. [arxiv]B. F. LourenĂ§o, V. Roshchina, J. Saunderson,

*Amenable cones are particularly nice*, November 2020. [arxiv]J. Saunderson, V. Chandrasekaran,

*Terracini Convexity*, October 2020. [arxiv]H. Fawzi, J. Gouveia, P. A. Parrilo, J. Saunderson, R. R. Thomas,

*Lifting for Simplicity: Concise Descriptions of Convex Sets*, February 2020. [arxiv]R. Sanyal, J. Saunderson,

*Spectral Polyhedra*, January 2020. [arxiv]R. P. Adams, J. Pennington, M. J. Johnson, J. Smith, Y. Ovadia, B. Patton, J. Saunderson,

*Estimating the Spectral Density of Large Implicit Matrices*, February 2018. [arxiv]

N. Shinde, V. Narayanan, J. Saunderson,

*Memory-efficient structured convex optimization via extreme point sampling*, SIAM Journal on Mathematics of Data Science, Vol 3, No. 3, 787–814, 2021. [doi] [arxiv]J. Saunderson,

*Limitations on the expressive power of convex cones without long chains of faces*, SIAM Journal on Optimization, Vol 30, No. 1, pp. 1033–1047, 2020. [doi] [arxiv] [BIRS talk]J. Saunderson,

*Certifying polynomial nonnegativity via hyperbolic optimization*, SIAM Journal on Applied Algebra and Geometry, Vol 3, No. 4, pp. 661–690, 2019. [doi] [arxiv] [YouTube]N. Veldt, D. Gleich, A. Wirth, J. Saunderson,

*Metric-Constrained Optimization for Graph Clustering Algorithms*, SIAM Journal on Mathematics of Data Science, Vol. 1, No. 2, pp. 333–355, 2019. [doi] [arxiv] (Previous title:*A Projection Method for Metric-Constrained Optimization*)H. Fawzi, J. Saunderson, P. A. Parrilo,

*Semidefinite approximations of the matrix logarithm*, Foundations of Computational Mathematics, Vol 19, No. 2, pp. 259–296, 2019. [doi] [arxiv] [code] Recipient of SIAM Activity Group on Optimization Best Paper Prize 2020.

R. Eghbali, J. Saunderson, M. Fazel,

*Competitive Online Algorithms for Resource Allocation over the Positive Semidefinite Cone*, Mathematical Programming Series B, Vol. 170, No. 1, pp. 267–292, 2018 [doi] [arxiv]J. Saunderson,

*A spectrahedral representation of the first derivative relaxation of the positive semidefinite cone*, Optimization Letters, Vol. 12, No. 7, pp. 1475–1486, 2018 [doi] [arxiv] [YouTube] (Correction: For corollary 2 to hold, the matrix V_{n}on page 1484 should have orthonormal columns.)A. Raymond, J. Saunderson, M. Singh, R. R. Thomas,

*Symmetric Sums of Squares over k-Subset Hypercubes*, Mathematical Programming Series A, Vol. 167, No. 2, pp. 315–354, 2018 [doi] [arxiv]H. Fawzi, J. Saunderson,

*Lieb's concavity theorem, matrix geometric means, and semidefinite optimization*, Linear Algebra and its Applications, Vol. 513, pp. 240–263, 2017 [doi] [arxiv] [matlab code]H. Fawzi, J. Saunderson, P. A. Parrilo,

*Equivariant semidefinite lifts of regular polygons*, Mathematics of Operations Research, Vol. 42, No. 2, pp. 472–494, 2017 [doi] [arxiv]H. Fawzi, J. Saunderson, P. A. Parrilo,

*Sparse sums of squares on finite abelian groups and improved semidefinite lifts*, Mathematical Programming Series A, Vol. 160, No. 1, pp. 149–191, 2016 [doi] [arxiv]J. Saunderson, P. A. Parrilo, A. S. Willsky,

*Convex solution to a joint attitude and spin-rate estimation problem*, J. Guidance, Control, and Dynamics, Vol. 39, No. 1, pp. 118–127, 2016 [doi] [arxiv]H. Fawzi, J. Saunderson, P. A. Parrilo,

*Equivariant semidefinite lifts and sum-of-squares hierarchies*, SIAM J. Optimization, Vol. 25, No. 4, pp. 2212–2243, 2015 [doi] [arxiv]J. Saunderson, P. A. Parrilo, A. S. Willsky,

*Semidefinite descriptions of the convex hull of rotation matrices*, SIAM J. Optimization, Vol. 25, No. 3, pp. 1314–1343, 2015 [doi] [arxiv] [pdf]J. Saunderson, P. A. Parrilo,

*Polynomial-sized semidefinite representations of derivative relaxations of spectrahedral cones*, Mathematical Programming Series A, Vol. 153, No. 2, pp. 309–331, 2015 [doi] [arxiv] [pdf]J. Saunderson, V. Chandrasekaran, P. A. Parrilo, A. S. Willsky,

*Diagonal and low-rank matrix decompositions, correlation matrices, and ellipsoid fitting*, SIAM J. Matrix Analysis and Applications, Vol. 33, No. 4, pp. 1395–1416, 2012 [doi] [arxiv] [pdf] [bibtex]

A. A. Ahmadi, G. Hall, A. Papachristodoulou, J. Saunderson, Y. Zheng,

*Improving efficiency and scalability of sum of squares optimization: recent advances and limitations*, Proc. 56th IEEE Conference on Decision and Control (CDC), Dec 2017 [doi] [arxiv]A. Jalali, J. Saunderson, M. Fazel, B. Hassibi,

*Error bounds for Bregman Denoising and Structured Natural Parameter Estimation*, Proc. 2017 IEEE International Symposium on Information Theory (ISIT), June 2017 [doi]J. Saunderson, M. Fazel, B. Hassibi,

*Simple algorithms and guarantees for low rank matrix completion over F*, Proc. 2016 IEEE International Symposium on Information Theory (ISIT), July 2016 [doi]_{2}K. Jaganathan, J. Saunderson, M. Fazel, Y. C. Eldar, B. Hassibi,

*Phaseless super-resolution using masks*, Proc. 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), March 2016 [doi]H. Fawzi, J. Saunderson, P. A. Parrilo,

*Sparse sum-of-squares certificates on finite abelian groups*, Proc. 54th IEEE Conference on Decision and Control (CDC), December 2015 [doi]J. Saunderson, P. A. Parrilo, A. S. Willsky,

*Semidefinite relaxations for optimization problems over rotation matrices*, Proc. 53rd IEEE Conference on Decision and Control (CDC), December 2014 [doi] [pdf]J. Saunderson, P. A. Parrilo, A. S. Willsky,

*Diagonal and low-rank decompositions and fitting ellipsoids to random points*, Proc. 52nd IEEE Conference on Decision and Control (CDC), December 2013 [doi] [pdf] [bibtex]M. J. Johnson, J. Saunderson, A. S. Willsky,

*Analyzing Hogwild Parallel Gaussian Gibbs Sampling*, Advances in Neural Information Processing Systems (NIPS), December 2013 [url] [pdf] [bibtex]J. Saunderson, V. Chandrasekaran, P. A. Parrilo, A. S. Willsky,

*Tree-structured statistical modeling via convex optimization*, Proc. 50th IEEE Conference on Decision and Control (CDC), December 2011 [doi] [pdf] [bibtex]T. Coleman, J. Saunderson, A. Wirth,

*A local-search 2-approximation for 2-correlation-clustering*, Proc. European Symposium on Algorithms (ESA), September 2008 [doi] [pdf] [bibtex]T. Coleman, J. Saunderson, A. Wirth,

*Spectral clustering with inconsistent advice*, Proc. International Conference on Machine Learning (ICML), June 2008 [doi] [pdf] [bibtex]

PhD Thesis:

*Semidefinite representations with applications in estimation and inference*, April 2015

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Honour's Thesis:

*Mostow's rigidity theorem*, November 2008

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*Monash University*

ECE4132 Control system design: 2018–2021

ECE2111 Signals and systems: 2017–2020

ECE3062 Electronic systems and control: 2016–2017

*MIT*

Fall 2011: TA for 6.255/15.093J Optimization Methods

*Divundu combined school*

January 2009 – June 2009: Teacher of grades 8–10 mathematics and physical science

*University of Melbourne*

Semester 2, 2008: Lab demonstrator for 431-461 Signal Processing 2

Semester 1, 2008: Lab demonstrator for 431-335 Signal Processing 1

Semester 1, 2007: Lab demonstrator for 431-325 Stochastic Signals and Systems

Semester 2, 2006, 2007: Tutor for 431-221 Fundamentals of Signals and Systems