44 citations · 158 across the 15 of their papers we have counts for
16 papers
Distributed Optimization, Averaging via ADMM, and Network Topology
Guilherme França, José Bento
There has been an increasing necessity for scalable optimization methods, especially due to the explosion in the size of datasets and model complexity in modern machine learning ap…
Gradient flows and proximal splitting methods: A unified view on accelerated and stochastic optimization
Guilherme França, Daniel P. Robinson, René Vidal
Optimization is at the heart of machine learning, statistics and many applied scientific disciplines. It also has a long history in physics, ranging from the minimal action princip…
A Nonsmooth Dynamical Systems Perspective on Accelerated Extensions of ADMM
Guilherme França, Daniel P. Robinson, René Vidal
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth…
ADMM and Accelerated ADMM as Continuous Dynamical Systems
Guilherme França, Daniel P. Robinson, René Vidal
Recently, there has been an increasing interest in using tools from dynamical systems to analyze the behavior of simple optimization algorithms such as gradient descent and acceler…
An Explicit Convergence Rate for Nesterov's Method from SDP
Sam Safavi, Bikash Joshi, Guilherme França +1
The framework of Integral Quadratic Constraints (IQC) introduced by Lessard et al. (2014) reduces the computation of upper bounds on the convergence rate of several optimization al…
Kernel k-Groups via Hartigan's Method
Guilherme França, Maria L. Rizzo, Joshua T. Vogelstein
Energy statistics was proposed by Sz\' ekely in the 80's inspired by Newton's gravitational potential in classical mechanics and it provides a model-free hypothesis test for equali…
Markov Chain Lifting and Distributed ADMM
Guilherme França, José Bento
The time to converge to the steady state of a finite Markov chain can be greatly reduced by a lifting operation, which creates a new Markov chain on an expanded state space. For a…
Two-dimensional Bose and Fermi gases beyond weak coupling
Guilherme Franca, Andre LeClair, Joshua Squires
Using a formalism based on the two-body S-matrix we study two-dimensional Bose and Fermi gases with both attractive and repulsive interactions. Approximate analytic expressions, va…
Tuning Over-Relaxed ADMM
Guilherme França, José Bento
The framework of Integral Quadratic Constraints (IQC) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to a semi-definite program…
An Explicit Rate Bound for the Over-Relaxed ADMM
Guilherme França, José Bento
The framework of Integral Quadratic Constraints of Lessard et al. (2014) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to semi-…
Some Riemann Hypotheses from Random Walks over Primes
Guilherme França, André LeClair
The aim of this article is to investigate how various Riemann Hypotheses would follow only from properties of the prime numbers. To this end, we consider two classes of -functio…
Transcendental equations satisfied by the individual zeros of Riemann , Dirichlet and modular -functions
Guilherme França, André LeClair
We consider the non-trivial zeros of the Riemann -function and two classes of -functions; Dirichlet -functions and those based on level one modular forms. We show that the…
On the validity of the Euler product inside the critical strip
Guilherme França, André LeClair
The Euler product formula relates Dirichlet functions to an infinite product over primes, and is known to be valid for , where it converges absolutely. We prov…
On the zeros of L-functions
Guilherme França, André LeClair
We generalize our recent construction of the zeros of the Riemann -function to two infinite classes of -functions, Dirichlet -functions and those based on level one modula…
Statistical and other properties of Riemann zeros based on an explicit equation for the -th zero on the critical line
Guilherme França, André LeClair
We show that there are an infinite number of Riemann zeros on the critical line, enumerated by the positive integers , whose ordinates can be obtained as the solution…
Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy
J. F. Gomes, Guilherme S. França, A. H. Zimerman
We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solut…