Publications related to Derivatives with respect to metrics and applications: subgradient marching algorithm

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

We prove a version of Myers-Steenrod's theorem for Finsler manifolds under the minimal regularity hypothesis. In particular we show that an isometry between C-k,C-alpha-smooth (or partially smooth) Finsler metrics, with k + alpha > 0, k is an element of N ...

Amer Mathematical Soc2017

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

Nicolas Henri Bernard Flammarion

We consider the minimization of a function deﬁned on a Riemannian manifold M accessible only through unbiased estimates of its gradients. We develop a geometric framework to transform a sequence of slowly converging iterates generated from stochastic gradi ...

2017

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Tudor Ratiu

Bi-Jacobi fields are generalized Jacobi fields, and are used to efficiently compute approximations to Riemannian cubic splines in a Riemannian manifold M. Calculating bi-Jacobi fields is straightforward when M is a symmetric space such as bi-invariant SO(3 ...

Int Press Boston, Inc2016

Robust Smith Predictor Design for Time-Delay Systems with H∞ Performance

Alireza Karimi, Achille Nicoletti, Vinicius De Oliveira

A new method for robust fixed-order H∞ controller design for uncertain time-delay systems is presented. It is shown that the H∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a linearly para ...

Springer2015

A Data-Driven Approach in Designing RST Controllers with H∞ Performance via Convex Optimization

Alireza Karimi, Achille Nicoletti, Zlatko Emedi

In this paper, a new method for designing robust fixed-order

\mathcal{H}_{\infty}

discrete-time controllers is presented. The controller structure is a two-degree of freedom polynomial controller of the

RST

type. A data-driven approach is implemented f ...

IEEE2015

The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative-Type Metrics into ℓ_1

Nisheeth Vishnoi

In this article, we disprove a conjecture of Goemans and Linial; namely, that every negative type metric embeds into ℓ1 with constant distortion. We show that for an arbitrarily small constant δ > 0, for all large enough n, there is an n-point negative ...

Association for Computing Machinery2015

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Martins Bruveris, Martin Bauer

In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space equipped with the homogeneous Sobolev metric of order one is a flat space in the sense of Riemannian geometry, as it is isometric to an ...

Springer Verlag2014

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

Martins Bruveris, Martin Bauer

This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics th ...

Springer Verlag2014

Constructing reparameterization invariant metrics on spaces of plane curves

Martins Bruveris, Martin Bauer

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics ...

Elsevier2014

H∞ smith predictor design for time-delayed MIMO systems via convex optimization

Alireza Karimi, Achille Nicoletti

A new method for robust fixed-order H∞ controller design for uncertain time-delayed MIMO systems is presented. It is shown that the H∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a linear ...

IEEE2014

Derivatives with respect to metrics and applications: subgradient marching algorithm

Graph Chatbot

Chat with Graph Search

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Robust Smith Predictor Design for Time-Delay Systems with H∞ Performance

A Data-Driven Approach in Designing RST Controllers with H∞ Performance via Convex Optimization

The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative-Type Metrics into ℓ_1

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

Constructing reparameterization invariant metrics on spaces of plane curves

H∞ smith predictor design for time-delayed MIMO systems via convex optimization

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative-Type Metrics into ℓ_1

Robust Smith Predictor Design for Time-Delay Systems with H∞ Performance

A Data-Driven Approach in Designing RST Controllers with H∞ Performance via Convex Optimization

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

Constructing reparameterization invariant metrics on spaces of plane curves

H∞ smith predictor design for time-delayed MIMO systems via convex optimization

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups