Hamza Fawzi
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Publications
Quantum information
Defining quantum divergences using convex optimization
(with Omar Fawzi),
Quantum
.
Computing conditional entropies for quantum correlations
(with Peter Brown and Omar Fawzi),
Nature Communications
.
The geometric Rényi divergence and its applications in quantum channel capacities
(with Kun Fang),
accepted in Communications in Mathematical Physics
.
The set of separable states has no finite semidefinite representation except in dimension 3x2
,
accepted in Communications in Mathematical Physics
.
Efficient optimization of the quantum relative entropy
(with Omar Fawzi),
Journal of Physics A
(
erratum
)
(
arXiv version
with the title "Relative entropy optimization in quantum information theory via semidefinite programming approximations")
The sum-of-squares hierarchy on the sphere, and applications in quantum information theory
(with Kun Fang),
Mathematical Programming
.
Machine learning
Learning dynamic polynomial proofs
(with Alhussein Fawzi, Mateusz Malinowski, Omar Fawzi),
NeurIPS 2019 (spotlight)
.
Adversarial vulnerability for any classifier
(with Alhussein Fawzi and Omar Fawzi),
NeurIPS 2018
.
Optimization theory
Sum-of-squares proofs of logarithmic Sobolev inequalities on finite Markov chains
(with Oisín Faust),
preprint
.
On polyhedral approximations of the positive semidefinite cone
,
Mathematics of Operations Research
.
A lower bound on the positive semidefinite rank of convex bodies
(
arXiv link
),
SIAM Journal on Applied Algebra and Geometry
Hamza Fawzi, Mohab Safey El Din.
Semidefinite approximations of the matrix logarithm
(
arXiv link
),
Foundations of Computational Mathematics
Hamza Fawzi, James Saunderson, Pablo A. Parrilo.
Matlab code
Recipient of
SIAM Activity Group on Optimization Best Paper Prize 2020
On representing the positive semidefinite cone using the second-order cone
,
Mathematical Programming
.
(PhD thesis)
Power and limitations of convex formulations via linear and semidefinite programming lifts
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology
Lieb's concavity theorem, matrix geometric means, and semidefinite optimization
(
corrigendum
)
Hamza Fawzi, James Saunderson,
Linear Algebra and its Applications
, vol.513, pp.240--263, 2017.
Matlab code
Sparse sums of squares on finite abelian groups and improved semidefinite lifts
Hamza Fawzi, James Saunderson, Pablo A. Parrilo,
Mathematical Programming Series A
, vol.160, no.1, pp.149--191, 2016
Equivariant semidefinite lifts of regular polygons
Hamza Fawzi, James Saunderson, Pablo A. Parrilo,
Mathematics of Operations Research
, vol.42, no.2, pp.472--494, 2017
Equivariant semidefinite lifts and sum-of-squares hierarchies
Hamza Fawzi, James Saunderson, Pablo A. Parrilo
SIAM Journal on Optimization
, vol.25, no.4, pp.2212--2243, 2015.
(
Erratum
)
Rational and real positive semidefinite rank can be different
João Gouveia, Hamza Fawzi, Richard Z. Robinson,
Operations Research Letters
Positive semidefinite rank
Hamza Fawzi, João Gouveia, Pablo A. Parrilo, Richard Z. Robinson, Rekha R. Thomas
Mathematical Programming Series B, special issue on "Lifts of Convex Sets"
, vol.153, no.1, pp.133--177, 2015
Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank
Hamza Fawzi, Pablo A. Parrilo
Mathematical Programming Series A, vol.158, no.1, pp.417--465, 2016
Accompanying Matlab code:
tauplus_sos.m
,
tauplus_sos_tensor.m
,
taucp_sos.m
Lower bounds on nonnegative rank via nonnegative nuclear norms
Hamza Fawzi, Pablo A. Parrilo
Mathematical Programming Series B, special issue on "Lifts of Convex Sets"
, vol.153, no.1, pp.41--66, 2015
(The same paper previously had the title "New lower bounds on nonnegative rank using conic programming")
Accompanying Matlab code
Exponential lower bounds on fixed-size psd rank and semidefinite extension complexity
,
arXiv preprint 2013
Hamza Fawzi, Pablo A. Parrilo
Control theory
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 conference 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)