Massachusetts Institute of Technology

77 Massachusetts Avenue, Room 32-D762

CAMBRIDGE MA 02139-4307

Hamza Fawzi

I am a third-year PhD student in the EECS department at MIT working with Prof. Pablo Parrilo.

I obtained my M.S. from UCLA working under the supervision of Prof. Paulo Tabuada. Before that, I was at Mines ParisTech in France where I studied engineering and applied mathematics.

My research interests are in the broad area of convex optimization.

Publications
**Sparse sum-of-squares certificates on finite abelian groups**, *arXiv preprint 2015*

Hamza Fawzi, James Saunderson, Pablo A. Parrilo

**Equivariant semidefinite lifts of regular polygons**, *arXiv preprint 2014*

Hamza Fawzi, James Saunderson, Pablo A. Parrilo

**Positive semidefinite rank**, [arXiv version]

Hamza Fawzi, Joćo Gouveia, Pablo A. Parrilo, Richard Z. Robinson, Rekha R. Thomas

*Mathematical Programming Series B, special issue on "Lifts of Convex Sets"*

**Rational and real positive semidefinite rank can be different**, *arXiv preprint 2014*

Joćo Gouveia, Hamza Fawzi, Richard Z. Robinson

**Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank**, *[arXiv version]*

Hamza Fawzi, Pablo A. Parrilo

*Mathematical Programming Series A*

Accompanying Matlab code: tauplus_sos.m, tauplus_sos_tensor.m, taucp_sos.m

**Equivariant semidefinite lifts and sum-of-squares hierarchies**, *arXiv preprint 2013*

Hamza Fawzi, James Saunderson, Pablo A. Parrilo

**Exponential lower bounds on fixed-size psd rank and semidefinite extension complexity**, *arXiv preprint 2013*

Hamza Fawzi, Pablo A. Parrilo

**Lower bounds on nonnegative rank via nonnegative nuclear norms** [arXiv version]

Hamza Fawzi, Pablo A. Parrilo

*Mathematical Programming Series B, special issue on "Lifts of Convex Sets"*

(The same paper previously had the title "New lower bounds on nonnegative rank using conic programming")

Accompanying Matlab code

**Secure estimation and control for cyber-physical systems under adversarial attacks**

Hamza Fawzi, Paulo Tabuada, Suhas Diggavi

*IEEE Transactions on Automatic Control*, vol.59, no.6, pp.1454--1467, June 2014

Preliminary versions of this paper:

- Security for control systems under sensor and actuator attacks, IEEE CDC 2012 (doi)
- Secure state-estimation for dynamical systems under active adversaries, IEEE Allerton Conference 2011 (doi)

**An improved self-triggered implementation for linear controllers (doi)**

Jose Araujo, Hamza Fawzi, Manuel Mazo Jr., Paulo Tabuada and Karl Henrik Johansson

*Proceedings of the 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys 2012)*

- Spring 2015: TA for 6.252/15.084 Nonlinear programming
- Spring 2014: TA for 6.256 Algebraic Techniques and Semidefinite Optimization

Sparse sum-of-squares certificates on finite abelian groups

presented at Caltech Computing and Mathematical Sciences, UCLA Electrical Engineering, GeorgiaTech Mathematics (Algebra Seminar) - March 2015

Equivariant semidefinite lifts and sum-of-squares hierarchies

presented at ISMP 2015 (Pittsburgh).

Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank

presented at SIAM Conference on Optimization 2014 (San Diego) and Applied Algebra Days 2 (University of Wisconsin, Madison)

Lower bounds on nonnegative rank via nonnegative nuclear norms

presented at Dagstuhl Seminar on "Communication Complexity, Linear Optimization, and lower bounds for the nonnegative rank of matrices" and ICCOPT 2013 (Lisbon, Portugal)