Ces dernières années ont vu une résurgence de l’algorithme de Frank-Wolfe (FW) (également connu sous le nom de méthodes de gradient conditionnel) dans l’optimisation clairsemée et les problèmes d’apprentissage automatique à grande échelle avec des objectifs convexes lisses. Par rapport aux méthodes de gradient projeté ou proximal, une telle méthode sans projection permet d’économiser le coût de calcul des projections orthogonales sur l’ensemble de contraintes. Parallèlement, FW propose également des solutions à structure clairsemée. Malgré ces propriétés prometteuses, FW ne bénéficie pas des taux de convergence optimaux obtenus par les méthodes accélérées basées sur la projection. Nous menons une enquête dé- taillée sur les essais récents pour accélérer FW dans différents contextes et soulignons où se situe la difficulté lorsque l’on vise des taux linéaires globaux en théorie. En outre, nous fournissons une direction prometteuse pour accélérer FW sur des ensembles fortement convexes en utilisant des techniques d’intervalle de dualité et une nouvelle notion de régularité. D’autre part, l’algorithme FW est une covariante affine et bénéficie de taux de convergence accélérés lorsque l’ensemble de contraintes est fortement convexe. Cependant, ces résultats reposent sur des hypothèses dépendantes de la norme, entraînant généralement des bornes invariantes non affines, en contradiction avec la propriété de covariante affine de FW. Dans ce travail, nous introduisons de nouvelles hypothèses structurelles sur le problème (comme la régularité directionnelle) et dérivons une analyse affine invariante et indépendante de la norme de Frank-Wolfe. Sur la base de notre analyse, nous proposons une recherche par ligne affine invariante. Fait intéressant, nous montrons que les recherches en ligne classiques utilisant la régularité de la fonction objectif convergent étonnamment vers une taille de pas invariante affine, malgré l’utilisation de normes dépendantes de l’affine dans le calcul des tailles de pas. Cela indique que nous n’avons pas nécessairement besoin de connaître à l’avance la structure des ensembles pour profiter du taux accéléré affine-invariant. Dans un autre axe de recherche, nous étudions les algorithmes au-delà des méthodes du premier ordre. Les techniques Quasi-Newton approchent le pas de Newton en estimant le Hessien en utilisant les équations dites sécantes. Certaines de ces méthodes calculent le Hessien en utilisant plusieurs équations sécantes mais produisent des mises à jour non symétriques. D’autres schémas quasi-Newton, tels que BFGS, imposent la symétrie mais ne peuvent pas satisfaire plus d’une équation sécante. Nous proposons un nouveau type de mise à jour symétrique quasi-Newton utilisant plusieurs équations sécantes au sens des moindres carrés. Notre approche généralise et unifie la conception de mises à jour quasi-Newton et satisfait des garanties de robustesse prouvables. / Recent years have witnessed a resurgence of the Frank-Wolfe (FW) algorithm, also known as conditional gradient methods, in sparse optimization and large-scale machine learning problems with smooth convex objectives. Compared to projected or proximal gradient methods, such projection-free method saves the computational cost of orthogonal projections onto the constraint set. Meanwhile, FW also gives solutions with sparse structure. Despite of these promising properties, FW does not enjoy the optimal convergence rates achieved by projection-based accelerated methods. On the other hand, FW algorithm is affine-covariant, and enjoys accelerated convergence rates when the constraint set is strongly convex. However, these results rely on norm-dependent assumptions, usually incurring non-affine invariant bounds, in contradiction with FW’s affine-covariant property. In this work, we introduce new structural assumptions on the problem (such as the directional smoothness) and derive an affine in- variant, norm-independent analysis of Frank-Wolfe. Based on our analysis, we pro- pose an affine invariant backtracking line-search. Interestingly, we show that typical back-tracking line-search techniques using smoothness of the objective function surprisingly converge to an affine invariant stepsize, despite using affine-dependent norms in the computation of stepsizes. This indicates that we do not necessarily need to know the structure of sets in advance to enjoy the affine-invariant accelerated rate. Additionally, we provide a promising direction to accelerate FW over strongly convex sets using duality gap techniques and a new version of smoothness. In another line of research, we study algorithms beyond first-order methods. Quasi-Newton techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other quasi- Newton schemes, such as BFGS, enforce symmetry but cannot satisfy more than one secant equation. We propose a new type of quasi-Newton symmetric update using several secant equations in a least-squares sense. Our approach generalizes and unifies the design of quasi-Newton updates and satisfies provable robustness guarantees.

This study focuses on the investigation and deconstruction of the phenomena of the South African dystopian society, as reflected in the novels of Lauren Beukes and films by Neill Blomkamp. The characteristics and signifiers of a uniquely South African dystopian society are established and investigated through a posthuman lens. The theoretical framework of this study is principally concerned with the critical posthuman writings of Rosi Braidotti, Donna Haraway and, to a lesser extent, Cary Wolfe. Feminism and post-colonialism, and their influences on posthuman theory, are applied as the secondary theoretical framework, in this study. The study is practice led, with the study of the literature serving as mutually informative to the execution of a body of work centred on the dystopian theme. The paintings are intended to be metonyms for the wide range of manifestations of social decline evident in contemporary South African narratives. / Arts and Music / M.A. (Visual Arts)

Rex Stout maintained his popular readership despite the often controversial and radical political content expressed in his detective fiction. His political ideals often made him many enemies. Stances such as his ardent opposition to censorship, racism, Nazism, Germany, Fascism, Communism, McCarthyism, and the unfettered FBI were potentially offensive to colleagues and readers from various political backgrounds. Yet Stout attempted to present radical messages via the content of his detective fiction with subtlety. As a literary traditionalist, he resisted using his fiction as a platform for an often extreme political agenda. Where political messages are apparent in his work, Stout employs various techniques to mute potentially offensive messages. First, his hugely successful bantering Archie Goodwin-Nero Wolfe detective duo—a combination of both the lippy American and the tidy, sanitary British detective schools—fosters exploration, contradiction, and conflict between political viewpoints. Archie often rejects or criticizes Wolfe's extreme political viewpoints. Second, Stout utilizes the contradictions between values that occur when the form of detective fiction counters his radical political messages. This suggests that the form of detective fiction (in this case the conventional patterns and attitudes reinforced by the genre) is as important as the content (in this case the muted political message or the lack of overt politics) in reinforcing or shaping political, economic, moral, and social viewpoints. An analysis of the novels The Black Mountain (1954) and The Doorbell Rang (1965) and the novellas "Not Quite Dead Enough" and "Booby Trap" (1944) from Stout's Nero Wolfe series demonstrates his use of detective fiction for both the expression of political viewpoints and the muting of those political messages.