DSpace Collection:http://hdl.handle.net/10316/155442020-06-03T15:50:15Z2020-06-03T15:50:15ZIntrinsic Schreier Split ExtensionsMontoli, AndreaRodelo, DianaVan der Linden, Timhttp://hdl.handle.net/10316/894552020-06-03T15:45:47Z2020-01-01T00:00:00ZTitle: Intrinsic Schreier Split Extensions
Authors: Montoli, Andrea; Rodelo, Diana; Van der Linden, Tim
Abstract: In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier split epimorphisms of monoids do. This gives rise to new examples of S-protomodular categories, and allows us to better understand the homological behaviour of monoids from a categorical perspective.2020-01-01T00:00:00ZFacets of congruence distributivity in Goursat categoriesGran, MarinoRodelo, DianaNguefeu, Idriss Tchoffohttp://hdl.handle.net/10316/894522020-06-03T15:17:05Z2020-01-01T00:00:00ZTitle: Facets of congruence distributivity in Goursat categories
Authors: Gran, Marino; Rodelo, Diana; Nguefeu, Idriss Tchoffo
Abstract: We give new characterisations of regular Mal'tsev categories with distributive lattice of equivalence relations through variations of the so-called Triangular Lemma and Trapezoid Lemma in universal algebra. We then give new characterisations of equivalence distributive Goursat categories (which extend 3-permutable varieties) through variations of the Triangular and Trapezoid Lemmas involving reflexive and positive relations.2020-01-01T00:00:00ZOn difunctionality of class relationsHoefnagel, MichaelJanelidze, ZurabRodelo, Dianahttp://hdl.handle.net/10316/894502020-06-03T14:09:16Z2020-01-01T00:00:00ZTitle: On difunctionality of class relations
Authors: Hoefnagel, Michael; Janelidze, Zurab; Rodelo, Diana
Abstract: For a given variety V of algebras, we define a class relation to be a binary relation R ⊆ S^2 which is of the form R = S^2 ∩ K for some congruence class K on A^2, where A is an algebra in V such that S ⊆ A. In this paper we study the following property of V: every reflexive class relation is an equivalence relation. In particular, we obtain equivalent characterizations of this property analogous to well-known equivalent characterizations of congruence-permutable varieties. This property determines a Mal’tsev condition on the variety and in a suitable sense, it is a join of Chajda’s egg-box property as well as Duda’s direct decomposability of congruence classes.2020-01-01T00:00:00ZComplexity of gradient descent for multiobjective optimizationFliege, JörgVaz, António Ismael FreitasVicente, Luís Nuneshttp://hdl.handle.net/10316/894432020-06-02T20:30:22Z2019-01-01T00:00:00ZTitle: Complexity of gradient descent for multiobjective optimization
Authors: Fliege, Jörg; Vaz, António Ismael Freitas; Vicente, Luís Nunes
Abstract: A number of first-order methods have been proposed for smooth multiobjective optimization for which some form of convergence to first-order criticality has been proved. Such convergence is global in the sense of being independent of the starting point. In this paper, we analyse the rate of convergence of gradient descent for smooth unconstrained multiobjective optimization, and we do it for non-convex, convex, and strongly convex vector functions. These global rates are shown to be the same as for gradient descent in single-objective optimization and correspond to appropriate worst-case complexity bounds. In the convex cases, the rates are given for implicit scalarizations of the problem vector function.2019-01-01T00:00:00Z