Concept

Semi-differentiability

Related publications (17)

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

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

Regularized Diffusion Adaptation via Conjugate Smoothing

Ali H. Sayed, Stefan Vlaski

The purpose of this article is to develop and study a decentralized strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution, ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...

2021

Forward-Backward Splitting for Optimal Transport Based Problems

Pascal Frossard, Guillermo Ortiz Jimenez, Mireille El Gheche, Hermina Petric Maretic, Effrosyni Simou

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regula ...

2020

Adaptive Gradient Descent without Descent

Konstantin Mishchenko

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Solvent-Aware Interfaces in Continuum Solvation

Nicola Marzari, Oliviero Andreussi, Francesco Nattino, Nicolas Georg Hörmann

Continuum models to handle solvent and electrolyte effects in an effective way have a long tradition in quantum-chemistry simulations and are nowadays also being introduced in computational condensed-matter and materials simulations. A key ingredient of co ...

AMER CHEMICAL SOC2019

Smoothing technique for nonsmooth composite minimization with linear operator

Volkan Cevher, Van Quang Nguyen

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap technique. In addition t ...

2017

A Sampling Theory for Non-Decaying Signals

Michaël Unser, Quy Ha Nguyen

The classical assumption in sampling and spline theories is that the input signal is square-integrable, which prevents us from applying such techniques to signals that do not decay or even grow at infinity. In this paper, we develop a sampling theory for m ...

2017

Dynamical Low Rank approximation of PDEs with random parameters

Eleonora Musharbash

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

EPFL2017

On linear and quadratic Lipschitz bounds for twice continuously differentiable functions

Dominique Bonvin, Grégory François, Gene Bunin

Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic bounds that are state ...

arXiv:1406.3991 [math.OC]2014

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