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Affine maximal hypersurfaces

An-Min Li, Fang Jia (2005)

Banach Center Publications

This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss affine Bernstein problems and complete constant mean curvature surfaces in equiaffine differential geometry.

Alcuni problemi matematici legati alla gestione ottima di un portafoglio

Maurizio Pratelli (2004)

Bollettino dell'Unione Matematica Italiana

In questa conferenza, vengono esposte le idee essenziali che stanno alla base del classico problema di gestire un portafoglio in modo da rendere massima l'utilità media. I metodi tipici del controllo stocastico sono confrontati con le idee della dualità convessa infinito-dimensionale.

All-at-once preconditioning in PDE-constrained optimization

Tyrone Rees, Martin Stoll, Andy Wathen (2010)

Kybernetika

The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...

Almost sure properties of controlled diffusions and worst case properties of deterministic systems

Martino Bardi, Annalisa Cesaroni (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We compare a general controlled diffusion process with a deterministic system where a second controller drives the disturbance against the first controller. We show that the two models are equivalent with respect to two properties: the viability (or controlled invariance, or weak invariance) of closed smooth sets, and the existence of a smooth control Lyapunov function ensuring the stabilizability of the system at an equilibrium.


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