Search

Over the past years, operator splitting methods have become ubiquitous for non-smooth optimization owing to their simplicity and efficiency. In this paper, we consider the Forward--Douglas--Rachford splitting method (FDR) [10,40], and study both global and local convergence rates of this method. For the global rate, we establish an $o(1/k)$ convergence rate in terms of a Bregman divergence suitably designed for the objective function. Moreover, when specializing to the case of Forward--Backward splitting method, we show that convergence rate of the objective function of the method is actually $o(1/k)$ for a large choice of the descent step-size. Then locally, based on the assumption that the non-smooth part of the optimization problem is partly smooth, we establish local linear convergence of the method. More precisely, we show that the sequence generated by FDR method first (i) identifies a smooth manifold in a finite number of iteration, and then (ii) enters a local linear convergence regime, which is for instance characterized in terms of the structure of the underlying active smooth manifold. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from applicative fields including, for instance, signal/image processing, inverse problems and machine learning.

L’articolo si focalizza sulla drammaturgia degli attori-autori della Commedia dell’Arte cercando di estrapolarne i tratti comuni. La produzione letteraria dei comici è imponente per quantità e varietà. Tuttavia è ovvio che la nostra attenzione si concentri soprattutto sugli scritti che hanno un rapporto diretto con il teatro, e che possiamo classificare grosso modo in tre categorie: la trattatistica, che può avere carattere apologetico (come La Supplica di Nicolò Barbieri) o teorico-normativo (come I Frutti delle moderne comedie di Pier Maria Cecchini); gli zibaldoni, o generici; e la drammaturgia, che può consistere di commedie distese come di scenari o soggetti. In questa saggio mi soffermo in particolare sulla drammaturgia a partire dagli scenari di Flaminio Scala. Aldilà delle distinzioni di genere (dramma romanzesco, commedia, farsa), sono individuabili alcuni scenari con azione complessa; altri dalla struttura più semplice e lineare; altri infine in cui ogni reale principio compositivo sembra saltare a favore di un susseguirsi casuale di situazioni diverse, ma canoniche. In questi ultimi testi prevale la comicità dell’azione, gli spazi per i lazzi e le scene topiche sono forse più ampi. Ma soprattutto il livello verbale viene subordinato a quello mimico-coreografico. Ciò detto, varrà la pena verificare da un lato se e in quale misura le opere drammatiche degli attori si inseriscano nella tradizione della drammaturgia ‘regolare’; e dall’altro se e fino a che punto utilizzino gli elementi specifici della commedia dell’arte e quindi, in particolare, le maschere.

We present an alternating forward–backward splitting method for solving linearly constrained structured optimization problems. The algorithm takes advantage of the separable structure and possibly asymmetric regularity properties of the objective functions involved. We also describe some applications to the study of non-Newtonian fluids and image reconstruction problems. We conclude with a numerical example, and its comparison with Condat’s algorithm. An acceleration heuristic is also briefly outlined.

In 1880, the first modern editor to publish a collection of commedia dell'arte scenarios noted, not without surprise, that ‘the earliest professional actors were almost all writers as well’. ‘Almost all’ is perhaps an exaggeration. Yet the literary production of comic players, and particularly that of the second and third generation of actors, is impressive for its quantity as well as its variety. It ranges from Giovan Paolo Fabbri's Capitoli alla Carlona and Adriano Valerini's historically important essay on the beauties of Verona, to the Rime of Isabella Andreini, in which she established a dialectic connection between the art of writing and that of the theatre:If you will read one daymy neglected verses, don't be taken in bythese feigned ardoursI am used to playing in dramatic love sceneswith such insincere passionswith lying and mock expressions.I unfold the Muses' high furoressometimes weeping in false sorrowsometimes singing with false pleasure.