We survey robust multigrid methods in the literature which have been developed in recent years for solving second order elliptic PDEs with nonsmooth coeecients. We highlight the key ideas of designing robust multigrid methods which are able to recover the usual multigrid eeciency for nonsmooth coeecient PDEs on structured or unstructured grids. In particular, we shall describe various approache...

Identifiability analysis is developed for linear dynamic systems evolving in a Hilbert space. Finite-dimensional sensing and actuation are assumed to be only available. Identifiability conditions for the transfer function of such a system is constructively addressed in terms of sufficiently nonsmooth controlled inputs. The introduced notion of a sufficiently nonsmooth input does not relate to a...

The classical trust region algorithm was extended to the nonsmooth minimization problem successful by Qi and Sun. Combining the trust region algorithm of Qi and Sun and the trust region algorithm with radius bounded below of Jiang for solving generalized complementarity problems, this paper present a new trust region algorithm with radius bounded below for the unconstrained nonsmooth optimizati...

New techniques of local sensitivity analysis for nonsmooth generalized equations are applied to the study of sequences of statistical estimates and empirical approximations to solutions of stochastic programs. Consistency is shown to follow from a certain local invertibility property, and asymptotic distributions are derived from a generalized implicit function theorem that characterizes asympt...

We study second-order nonlinear periodic systems driven by the vector p-Laplacian with a nonsmooth, locally Lipschitz potential function. Under minimal and natural hypotheses on the potential and using variational methods based on the nonsmooth critical point theory, we prove existence theorems and amultiplicity result. We conclude the paper with an existence theorem for the scalar problem, in ...

Variable structure-based robust compensators are general approaches to deal with uncertain nonlinear dynamic systems. The bang-bang (discontinuous-type) compensator and the saturation (continuous-type) compensator are the two common robust compensators used in variable structure controllers. This paper presents a comparative study of these two nonsmooth time-invariant robust compensators with a...

In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are teste...

in an axisymmetric co2-n2-h2o gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. to obtain a maximal small signal gain, some authors have tested several families of curves for ?. to find the most general solution for ?, an application of pontryagin’s principle led to the conjuncture that the optimal ? must consist o...

Steepest descent drives both theory and practice of nonsmooth optimization. We study slight relaxations of two influential notions of steepest descent curves — curves of maximal slope and solutions to evolution equations. In particular, we provide a simple proof showing that lower-semicontinuous functions that are locally Lipschitz continuous on their domains — functions playing a central role ...

Nonsmooth analysis, inequality constrained optimization and variational inequalities are involved in the modelling of unilateral contact problems. The corresponding theoretical and algorithmic tools, which are part of the area known as nonsmooth mechanics, are by no means classical. In general purpose software some of these tools (perhaps in a simplified way) are currently available. Two engine...