A relative-error inertial-relaxed inexact projective splitting algorithm

For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits from a combination of inertial and relaxation effects, which are both controlled by parameters within a certain range. We propose sufficient conditions on these parameters and study the interplay between them in order to guarantee weak convergence of sequences generated by our algorithm. Additionally, the proposed algorithm also benefits from inexact subproblem solution within a relative-error criterion. Simple numerical experiments on LASSO problems indicate some improvement when compared with previous (noninertial and exact) versions of projective splitting

University of Trieste

Appare opportuno riproporre un itinerario ideale attraverso la vita universitaria triestina con un volume che ne descriva, in chiave aggiornata, le innovazioni, l’articolazione strutturale, le ricerche scientifiche e le principali offerte di studio. Conoscere la Trieste accademica, con un testo anche in versione inglese, è quindi un obiettivo che ci poniamo in un’ottica di ampia diffusione del nostro ruolo culturale in un territorio vasto, che travalica i consueti confini nazionali, per estendersi alle nazioni limitrofe, all’ampio bacino danubiano, all’Europa intera, alla dimensione più propriamente internazionale e globale. D’altra parte, è noto come l’Università di Trieste sappia attrarre, da decenni, una quota sempre rilevante di studenti stranieri, certamente in virtù della sua ottimale posizione geografica, ma non solo, perché giungono, nella nostra città, giovani e studiosi provenienti ormai da tutti continenti. La città mercantile, crocevia di traffici e commerci, si può ben dire riviva oggi nella sua università e nelle altre prestigiose istituzioni scientifiche del territorio, con l’ateneo strettamente connesse, rinverdendo così una tradizione che ha sempre visto Trieste qualificato polo di attrazione dei migliori talenti culturali. L’auspicio più vivo è quindi che il lettore possa cogliere, attraverso il percorso di questo volume, affidato al dispiegarsi di idonee immagini, dati e testi illustrativi, le peculiarità più caratterizzanti di un ateneo dalle solide tradizioni, che non a caso celebra quest’anno il suo 90° anno di storia, eppure proiettato con slancio, direi molto giovanile, verso traguardi futuri di forte innovazione e cambiamento

Relative-error inexact versions of Douglas-Rachford and ADMM splitting algorithms

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-Graduação em Matemática Pura e Aplicada, Florianópolis, 2020.Nesta tese, propomos e analisamos novas versões do método Douglas-Rachford splitting (DRS) para operadores monótonos maximais e do alternating direction method of multipliers (ADMM) para otimização convexa. Inicialmente, apresentamos um método Douglas-Rachford splitting (DRS) inexato e um método Douglas-Rachford-Tseng forwardbackward (F-B) splitting para resolver inclusões monótonas de dois e quatro operadores, respectivamente. Provamos complexidade computacional em iteração, tanto no sentido pontual quanto no sentido ergódico, mostrando que ambos os algoritmos admitem duas iterações diferentes: uma que pode ser incorporada ao hybrid proximal extragradient (HPE) method de Solodov e Svaiter, para a qual a complexidade em iteração é conhecida desde o trabalho de Monteiro e Svaiter, e outra que exige uma análise em separado. Em seguida, estudamos o comportamento assintótico de novas variantes dos algoritmos DRS e ADMM, ambos com efeito de relaxação e inércia, e com critério de erro relativo para os subproblemas. Por fim, com objetivo de demonstrar a aplicabilidade dos métodos propostos neste trabalho, realizamos experimentos numéricos aplicando nosso método ADMM (relaxado e com inércia) aos problemas LASSO e regressão logística.Abstract: In this thesis, we propose and analyze new versions of the Douglas-Rachford splitting (DRS) method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. Firstly, we present an inexact DouglasRachford splitting (DRS) method and a Douglas-Rachford-Tseng?s forward-backward (F-B) splitting method for solving two-operator and four-operator monotone inclusions, respectively. We prove iteration-complexity bounds for both algorithms in the pointwise (non-ergodic) as well as in the ergodic sense by showing that they admit two different iterations: one that can be embedded into the Solodov and Svaiter?s hybrid proximal extragradient (HPE) method, for which the iteration-complexity is known since the work of Monteiro and Svaiter, and another one that demands a separate analysis. We also study the asymptotic behavior of new variants of the DRS and ADMM splitting methods, both under relaxation and inertial effects, and with inexact (relative-error) criterion for subproblems. To demonstrate the applicability of the proposed methods, we performed numerical experiments applying the ADMM (relaxed and inertial) on LASSO and logistic regression problems

Secretome analysis of Trichoderma atroviride T17 biocontrol of Guignardia citricarpa

The fungal species Guignardia citricarpa is an important pathogen in citriculture. Members of the fungal genus Trichoderma are recognized as biocontrol agents but studies on the interactions between both fungi are scarce. This study aimed to identify extracellular proteins secreted by Trichoderma atroviride T17 that are related to the control of G. citricarpa. Two-dimensional gel electrophoresis (2D) was used to study the patterns of proteins secreted by T. atroviride T17 in medium containing glucose (control) and in medium containing G. citricarpa GC3 inactivated mycelium. We identified 59 of the 116 spots differentially expressed (50.86%) by LC–MS/MS. Of these, we highlight the presence of glycoside hydrolases (CAZy families 3, 43, 54, 76 and 93), chitinase, mutanase, a-1,3-glucanase, a-1,2-mannosidase, carboxylic hydrolase ester, carbohydrate-binding module family 13, glucan 1,3-b-glucosidase, a-galactosidase and Neutral protease 2. These proteins are related to mycoparasitism processes, stimuli and therefore to the biological control of pathogens. The results obtained are in agreement with reports describing an increase in the secretion of proteins related to mycoparasitism and biological control and a reduction in the secretion of proteins related to the metabolism of Trichoderma species grown in the presence of the pathogen. Moreover, these results are pioneer in understanding T. atroviride interaction with G. citricarpa. For the first time, we identified potential candidate proteins that may have a role in the antagonism mechanism of G. citricarpa by T. atroviride T17. Thus our results shed a light into the molecular mechanisms that T. atroviride use to control G. citricarpa