93 citations · 322 across the 31 of their papers we have counts for
34 papers
Operator convexity along lines, self-concordance, and sandwiched Rényi entropies
Kerry He, James Saunderson, Hamza Fawzi
Barrier methods play a central role in the theory and practice of convex optimization. One of the most general and successful analyses of barrier methods for convex optimization, d…
QICS: Quantum Information Conic Solver
Kerry He, James Saunderson, Hamza Fawzi
We introduce QICS (Quantum Information Conic Solver), an open-source primal-dual interior point solver fully implemented in Python, which is focused on solving optimization problem…
Interior Point Methods for Structured Quantum Relative Entropy Optimization Problems
Kerry He, James Saunderson, Hamza Fawzi
Quantum relative entropy optimization refers to a class of convex problems in which a linear functional is minimized over an affine section of the epigraph of the quantum relative…
Compressive quantum waveform estimation
Alex Tritt, Joshua Morris, Christopher C. Bounds +3
Quantum waveform estimation, in which quantum sensors sample entire time series, promises to revolutionize the sensing of weak and stochastic signals, such as the biomagnetic impul…
Efficient Computation of the Quantum Rate-Distortion Function
Kerry He, James Saunderson, Hamza Fawzi
The quantum rate-distortion function plays a fundamental role in quantum information theory, however there is currently no practical algorithm which can efficiently compute this fu…
A Bregman Proximal Perspective on Classical and Quantum Blahut-Arimoto Algorithms
Kerry He, James Saunderson, Hamza Fawzi
The Blahut-Arimoto algorithm is a well-known method to compute classical channel capacities and rate-distortion functions. Recent works have extended this algorithm to compute vari…
Finite-State Semi-Markov Channels for Nanopore Sequencing
Brendon McBain, Emanuele Viterbo, James Saunderson
Nanopore sequencing is an emerging DNA sequencing technology that has been proposed for use in DNA storage systems. We propose the noisy nanopore channel model for nanopore sequenc…
Optimal self-concordant barriers for quantum relative entropies
Hamza Fawzi, James Saunderson
Quantum relative entropies are jointly convex functions of two positive definite matrices that generalize the Kullback-Leibler divergence and arise naturally in quantum information…
Spinsim: a GPU optimized python package for simulating spin-half and spin-one quantum systems
Alex Tritt, Joshua Morris, Joel Hochstetter +3
The Spinsim python package simulates spin-half and spin-one quantum mechanical systems following a time dependent Shroedinger equation. It makes use of numba.cuda, which is an LLVM…
Memory-Efficient Approximation Algorithms for Max-k-Cut and Correlation Clustering
Nimita Shinde, Vishnu Narayanan, James Saunderson
Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with G=(V,E) with n vertices, the methods with the best approximation guarantees for M…
A convex form that is not a sum of squares
James Saunderson
Every convex homogeneous polynomial (or form) is nonnegative. Blekherman has shown that there exist convex forms that are not sums of squares via a nonconstructive argument. We pro…
Hyperbolicity cones are amenable
Bruno F. Lourenço, Vera Roshchina, James Saunderson
Amenability is a notion of facial exposedness for convex cones that is stronger than being facially dual complete (or "nice") which is, in turn, stronger than merely being facially…
Amenable cones are particularly nice
Bruno F. Lourenço, Vera Roshchina, James Saunderson
Amenability is a geometric property of convex cones that is stronger than facial exposedness and assists in the study of error bounds for conic feasibility problems. In this paper…
Terracini Convexity
James Saunderson, Venkat Chandrasekaran
We present a generalization of the notion of neighborliness to non-polyhedral convex cones. Although a definition of neighborliness is available in the non-polyhedral case in the l…
Memory-efficient structured convex optimization via extreme point sampling
Nimita Shinde, Vishnu Narayanan, James Saunderson
Memory is a key computational bottleneck when solving large-scale convex optimization problems such as semidefinite programs (SDPs). In this paper, we focus on the regime in which…
Lifting for Simplicity: Concise Descriptions of Convex Sets
Hamza Fawzi, João Gouveia, Pablo A. Parrilo +2
This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the or…
Spectral Polyhedra
Raman Sanyal, James Saunderson
A "spectral convex set" is a collection of symmetric matrices whose range of eigenvalues form a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studi…
Certifying polynomial nonnegativity via hyperbolic optimization
James Saunderson
We describe a new approach to certifying the global nonnegativity of multivariate polynomials by solving hyperbolic optimization problems---a class of convex optimization problems…
Limitations on the expressive power of convex cones without long chains of faces
James Saunderson
A convex optimization problem in conic form involves minimizing a linear functional over the intersection of a convex cone and an affine subspace. In some cases, it is possible to…
A Projection Method for Metric-Constrained Optimization
Nate Veldt, David Gleich, Anthony Wirth +1
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give s…
Estimating the Spectral Density of Large Implicit Matrices
Ryan P. Adams, Jeffrey Pennington, Matthew J. Johnson +4
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of…
Competitive Online Algorithms for Resource Allocation over the Positive Semidefinite Cone
Reza Eghbali, James Saunderson, Maryam Fazel
We consider a new and general online resource allocation problem, where the goal is to maximize a function of a positive semidefinite (PSD) matrix with a scalar budget constraint.…
Improving Efficiency and Scalability of Sum of Squares Optimization: Recent Advances and Limitations
Amir Ali Ahmadi, Georgina Hall, Antonis Papachristodoulou +2
It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for…
A spectrahedral representation of the first derivative relaxation of the positive semidefinite cone
James Saunderson
If is an symmetric matrix, then the directional derivative of in the direction is the elementary symmetric polynomial of degree in the…