Research
My research is in mathematical optimization and its applications. On the foundational side,
I am particularly interested in the algebraic and geometric aspects of optimization models and algorithms.
I have worked on (or are currently working on) problems arising in areas such as statistical modelling,
signal processing, machine learning, power systems, astronautics, (quantum) information theory,
and quantum metrology.
Preprints
H. Fawzi, J. Saunderson, Optimal selfconcordant barriers for quantum relative entropies, May 2022.
[arxiv]
A. Tritt, J. Morris, J. Hochstetter, R. P. Anderson, J. Saunderson, L. D. Turner,
Spinsim: a GPU optimized python package for simulating spinhalf and spinone quantum systems, April 2022.
[arxiv]
B. F. LourenĂ§o, V. Roshchina, J. Saunderson,
Hyperbolicity cones are amenable, February 2021.
[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]
Journal Publications
S. Hadavi, J. Saunderson, A. MehriziSani, B. Bahrani,
A Planning Method for Synchronous Condensers in Weak Grids Using Semidefinite Optimization,
to appear in IEEE Transactions on Power Systems.
[doi]
B. F. LourenĂ§o, V. Roshchina, J. Saunderson,
Amenable cones are particularly nice, to appear in SIAM Journal on Optimization.
[arxiv]
J. Saunderson, A convex form that is not a sum of squares, to appear in Mathematics of Operations Research.
[arxiv]
[YouTube]
H. Fawzi, J. Gouveia, P. A. Parrilo, J. Saunderson, R. R. Thomas,
Lifting for Simplicity: Concise Descriptions of Convex Sets, to appear in SIAM Review. [arxiv]
[YouTube]
J. Saunderson, V. Chandrasekaran,
Terracini Convexity, Mathematical Programming Series A, 2022.
[doi]
[arxiv]
N. Shinde, V. Narayanan, J. Saunderson,
Memoryefficient 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,
MetricConstrained 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 MetricConstrained 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 kSubset 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 spinrate 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 sumofsquares 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, Polynomialsized 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 lowrank 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]
Refereed Conference Publications
B. McBain, E. Viterbo, J. Saunderson, FiniteState SemiMarkov Channels for Nanopore Sequencing,
To appear in Proc. 2022 IEEE International Symposium on Information Theory (ISIT), July 2022
[arxiv]
N. Shinde, V. Narayanan, J. Saunderson,
MemoryEfficient Approximation Algorithms for MaxkCut and Correlation Clustering,
To appear in Proc. 35th Advances in Neural Information Processing Systems (NeurIPS), December 2021
[arxiv]
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), December 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]
[pdf]
J. Saunderson, M. Fazel, B. Hassibi,
Simple algorithms and guarantees for low rank matrix completion over F_{2},
Proc. 2016 IEEE International Symposium on Information Theory (ISIT), July 2016
[doi]
[pdf]
K. Jaganathan, J. Saunderson, M. Fazel, Y. C. Eldar, B. Hassibi,
Phaseless superresolution 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 sumofsquares 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 lowrank 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,
Treestructured 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 localsearch 2approximation for 2correlationclustering,
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]
Theses
