Concept

Smoothness

Related publications (140)

Scalable constrained optimization

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

EPFL2024

Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations

Katie Sabrina Catherine Rosie Marsden

In this thesis we will present two results on global existence for nonlinear dispersive equations with data at or below the scaling regularity. In chapter 1 we take a probabilistic perspective to study the energy-critical nonlinear Schrödinger equation in ...

EPFL2024

SMOOTH APPROXIMATIONS FOR FULLY NONLINEAR NONLOCAL ELLIPTIC EQUATIONS

Xavier Fernandez-Real Girona

We show that any viscosity solution to a general fully nonlinear nonlocal elliptic equation can be approximated by smooth (C infinity) solutions. ...

Providence2023

Functional data analysis with rough sample paths?

Victor Panaretos, Neda Mohammadi Jouzdani

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

TAYLOR & FRANCIS LTD2023

ALMOST SURE SCATTERING OF THE ENERGY-CRITICAL NLS IN d > 6

Katie Sabrina Catherine Rosie Marsden

We study the energy-critical nonlinear Schrodinger equation with randomised initial data in dimensions d > 6. We prove that the Cauchy problem is almost surely globally well-posed with scattering for randomised supercritical initial data in H-s(Rd) wheneve ...

Springfield2023

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Nicolas Henri Bernard Flammarion

We consider the problem of sampling from a density of the form p(x) ? exp(-f (x) - g(x)), where f : Rd-+ R is a smooth function and g : R-d-+ R is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Hastings framework. Under ...

MICROTOME PUBL2022

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Jean Louis-Alexandre Fornerod

The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...

EPFL2022

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

UNDERGRAD: A Universal Black-Box Optimization Method with Almost Dimension-Free Convergence Rate Guarantees

Volkan Cevher, Kimon Antonakopoulos

Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem’s regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this regard, existin ...

2022

A geographical study of (M)over-bar(2)(P-2, 4)(main)

Francesca Carocci

We discuss criteria for a stable map of genus two and degree 4 to the projective plane to be smoothable, as an application of our modular desingularisation of (M) over bar (2,n)(P-r, d)(main) via logarithmic geometry and Gorenstein singularities. ...

WALTER DE GRUYTER GMBH2022

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