Nonsmooth calculus

A Proper Extension of Noether’s Symmetry Theorem for Nonsmooth Extremals of the Calculus of Variations

For nonsmooth Euler-Lagrange extremals, Noether’s conservation laws cease to be valid. We show that Emmy Noether’s theorem of the calculus of variations is still valid in the wider class of Lipschitz functions, as long as one restrict the Euler-Lagrange extremals to those which satisfy the DuBois-Reymond necessary condition. In the smooth case all EulerLagrange extremals are DuBois-Reymond extr...

A Proper Extension of Noether’s Symmetry Theorem for Nonsmooth Extremals of the Calculus of Variations

Nonsmooth Regularization

The purpose of this paper is to present to the Inverse Problems community some recent results regarding \nonsmooth", \edge preserving" regularization methods. Emphasis is placed on the penalized least squares (Tikhonov) regularization approach with penalty functionals of total variation type, although other nonquadratic penalty functionals are brieey discussed.

Nonsmooth Temporal Decompositions for Smooth and Nonsmooth Processes

Physical and mathematical principles of non-smooth decompositions of time, and their applications are discussed. These decompositions represent the temporal argument through the standard non-smooth motions of mechanical systems with impact interactions. As a result, singularities of behavior of physical systems are eliminated from their dynamics and described by the discontinuities of slope in ...

Nonsmooth H∞ synthesis

We develop nonsmooth optimization techniques to solve H∞ synthesis problems under additional structural constraints on the controller. Our approach avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems. The proposed framework is very versatile and can accommodate a number of challenging design problems including static, fixed...