Invariant variation problems

Affine Invariant Total Variation Models

This report relates to the field of image restorations and features extracting from noisy and blurred images. Since their introduction in a classical paper by Rudin, Osher and Fatemi [2], Total Variation (TV) minimising models have become one of the most popular and successful tools for image restorations. Whilst invariance under affine transformations is very important for many image processin...

Quasi-Invariant Optimal Control Problems

Quasi-Invariant Optimal Control Problems

We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are provided, in the direction which enlarges the scope of its application. We formulate a more general version of Noether’s theorem for optimal control problems, wh...

Some Problems in Invariant Theory

We present summaries of a number of research problems in invariant theory. These problems were posed during the organized problem sessions held during the April 2002, Kingston Ontario, Invariant Theory Workshop and Conference.

Invariant Variational Problems and Invariant Flows via Moving Frames

This paper reviews the moving frame approach to the construction of the invariant variational bicomplex. Applications include explicit formulae for the Euler-Lagrange equations of an invariant variational problem, and for the equations governing the evolution of differential invariants under invariant submanifold flows.