Publications related to Bootstrapping massive quantum field theories

An adaptive primal-dual framework for nonsmooth convex minimization

Volkan Cevher, Quoc Tran Dinh, Ahmet Alacaoglu

We propose a new self-adaptive and double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov’s smoothing technique via general Bregman distance functions. It self-adaptiv ...

2019

The S-matrix bootstrap. Part III: higher dimensional amplitudes

Jonathan Campbell Toledo

We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths relevant for the ela ...

SPRINGER2019

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Volkan Cevher, Ahmet Alacaoglu, Armin Eftekhari, Fabian Ricardo Latorre Gomez, Mehmet Fatih Sahin

We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is closely related to t ...

2019

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a

k\times k

submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix ...

MATHICSE2019

On the Averaged Green’s Function of an Elliptic Equation with Random Coefficients

Marius Christopher Lemm

We consider a divergence-form elliptic difference operator on the lattice Zd, with a coefficient matrix that is an i.i.d. perturbation of the identity matrix. Recently, Bourgain introduced novel techniques from harmonic analysis to prove the convergence of ...

2019

Multi-panel, on-single-chip Memristive Biosensing

Giovanni De Micheli, Sandro Carrara, Danilo Demarchi, Ioulia Tzouvadaki, Abuduwaili Tuoheti

Memristive biosensors have demonstrated excellent capabilities for ultrasensitive bio-detection. In the present work, memristive biosensing chips are designed, fabricated and implemented in a for the first time presented multi-panel on-chip detection for d ...

2019

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Damian Mateusz Straszak

Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most s ...

EPFL2018

Sharp sphere packings

Maryna Viazovska

In this talk we will speak about recent progress on the sphere packing problem. The packing problem can be formulated for a wide class of metric spaces equipped with a measure. An interesting feature of this optimization problem is that a slight change of ...

World Scientific Publishing2018

Convergence of the Exponentiated Gradient Method with Armijo Line Search

Volkan Cevher, Yen-Huan Li

Consider the problem of minimizing a convex differentiable function on the probability simplex, spectrahedron, or set of quantum density matrices. We prove that the expo-nentiated gradient method with Armijo line search always converges to the optimum, if ...

2018

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

Sebastian Urban Stich

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices i ...

2018

Bootstrapping massive quantum field theories

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An adaptive primal-dual framework for nonsmooth convex minimization

The S-matrix bootstrap. Part III: higher dimensional amplitudes

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

On the Averaged Green’s Function of an Elliptic Equation with Random Coefficients

Multi-panel, on-single-chip Memristive Biosensing

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Sharp sphere packings

Convergence of the Exponentiated Gradient Method with Armijo Line Search

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

The S-matrix bootstrap. Part III: higher dimensional amplitudes

Sharp sphere packings

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

Multi-panel, on-single-chip Memristive Biosensing

Convergence of the Exponentiated Gradient Method with Armijo Line Search

An adaptive primal-dual framework for nonsmooth convex minimization

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

On the Averaged Green’s Function of an Elliptic Equation with Random Coefficients