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 self-concordant 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 spin-half and spin-one quantum systems, April 2022. [arxiv]

  • B. F. Lourenço, 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. Mehrizi-Sani, B. Bahrani, A Planning Method for Synchronous Condensers in Weak Grids Using Semi-definite Optimization, to appear in IEEE Transactions on Power Systems. [doi]

  • B. F. Lourenço, 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, 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 Vn 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]

Refereed Conference Publications

  • B. McBain, E. Viterbo, J. Saunderson, Finite-State Semi-Markov 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, Memory-Efficient Approximation Algorithms for Max-k-Cut 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 F2, 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 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]

Theses

  • PhD Thesis: Semidefinite representations with applications in estimation and inference, April 2015
    [dspace] [pdf]

  • Master's Thesis: Subspace identification via convex optimization, May 2011
    [dspace] [pdf]

  • Honour's Thesis: Mostow's rigidity theorem, November 2008
    [pdf]