Canuto, Claudio:
Adaptive convex optimization in Banach spaces: a multilevel approach
Bollettino dell'Unione Matematica Italiana Serie 8 6-B (2003), fasc. n.2, p. 263-287, Unione Matematica Italiana (English)
pdf (505 Kb), djvu (385 Kb). | MR1988205 | Zbl 1177.42028
Sunto
In questo articolo, a prevalente carattere di rassegna, si considerano varie applicazioni del concetto di Approssimazione Nonlineare alla minimizzazione convessa adattativa. Dapprima, si ricordano alcuni concetti di base e si confrontano l'approssimazione lineare e quella nonlineare nel caso di tre basi funzionali notevoli: la base di Fourier, le basi degli elementi finiti e le basi di ondine. Successivamente, indichiamo come l'approssimazione nonlineare possa essere usata nella definizione di metodi adattativi per la risoluzione di problemi di minimizzazione astratta in spazi di Banach. Gli algoritmi risultanti, che impiegano sia basi di ondine sia basi di elementi finiti, risultano rigorosamente giustificabili e con proprietà di ottimalità dal punto di vista dell'efficienza. In questo ambito, si descrive con un qualche dettaglio un algoritmo di «steepest-descent» per discretizzazioni in ondine.
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Con il contributo del Ministero per i Beni e le Attività Culturali