Hamza Fawzi
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Publications
A subpolynomial-time algorithm for the free energy of one-dimensional quantum systems in the thermodynamic limit
(with Omar Fawzi and Samuel Scalet),
ITCS 2023, QIP 2023
Optimal self-concordant barriers for quantum relative entropies
(with James Saunderson),
preprint
.
Local Linear Convergence of Douglas-Rachford for Linear Programming: a Probabilistic Analysis
(with Oisín Faust),
ICML 2022
.
Strong data processing inequalities via sums of squares
(with Oisín Faust),
ISIT 2022
.
Semidefinite programming lower bounds on the squashed entanglement
(with Omar Fawzi),
QIP 2022 (merged with below)
Device-independent lower bounds on the conditional von Neumann entropy
(with Peter Brown and Omar Fawzi),
QIP 2022
.
Sum-of-squares proofs of logarithmic Sobolev inequalities on finite Markov chains
(with Oisín Faust),
preprint
.
Faster proximal algorithms for matrix optimization using Jacobi-based eigenvalue methods
(with Harry Goulbourne),
NeurIPS'21
.
Lifting for Simplicity: Concise Descriptions of Convex Sets
(with João Gouveia, Pablo Parrilo, James Saunderson, and Rekha Thomas),
SIAM Review
.
The set of separable states has no finite semidefinite representation except in dimension 3x2
,
Communications in Mathematical Physics
.
Defining quantum divergences using convex optimization
(with Omar Fawzi),
Quantum, QIP 2021 (merged with below)
.
Computing conditional entropies for quantum correlations
(with Peter Brown and Omar Fawzi),
Nature Communications, QIP 2021
.
The geometric Rényi divergence and its applications in quantum channel capacities
(with Kun Fang),
Communications in Mathematical Physics
.
The sum-of-squares hierarchy on the sphere, and applications in quantum information theory
(with Kun Fang),
Mathematical Programming
.
Learning dynamic polynomial proofs
(with Alhussein Fawzi, Mateusz Malinowski, Omar Fawzi),
NeurIPS 2019 (spotlight)
.
On polyhedral approximations of the positive semidefinite cone
,
Mathematics of Operations Research
.
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")
Adversarial vulnerability for any classifier
(with Alhussein Fawzi and Omar Fawzi),
NeurIPS 2018
.
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
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)