Capra-Convexity, Convex Factorization and Variational Formulations for the ℓ0 PseudonormSpringer Science and Business Media LLC - Tập 30 - Trang 597-619 - 2021
Jean-Philippe Chancelier, Michel De Lara
The so-called ℓ0 pseudonorm, or cardinality function, counts the number of nonzero components of a vector. In this paper, we analyze the ℓ0 pseudonorm by means of so-called Capra (constant along primal rays) conjugacies, for which the underlying source norm and its dual norm are both orthant-strictly monotonic (a notion that we formally introduce and that encompasses the ℓp-norms, but for the extr...... hiện toàn bộ
The Metric Integral of Set-Valued FunctionsSpringer Science and Business Media LLC - Tập 26 - Trang 867-885 - 2017
Nira Dyn, Elza Farkhi, Alona Mokhov
This paper introduces a new integral of univariate set-valued functions of bounded variation with compact images in
${\mathbb {R}}^d$
. The new integral, termed the metric integral, is defined using metric linear combinations of sets and is shown ...... hiện toàn bộ
PrefaceSpringer Science and Business Media LLC - Tập 26 - Trang 205-206 - 2018
Heinz H. Bauschke, Boris S. Mordukhovich, Claudia S. Sagastizábal, Michel A. Théra
Representative Functions, Variational Convergence and Almost ConvexitySpringer Science and Business Media LLC - Tập 32 - Trang 1-45 - 2024
A. Eberhard, R. Wenczel
We develop a new epi-convergence based on the use of bounded convergent nets on the product topology of the strong topology on the primal space and weak star topology on the dual space of a general real Banach space. We study the propagation of the associated variational convergences through conjugation of convex functions defined on this product space. These results are then applied to the proble...... hiện toàn bộ
Morse Decompositions for Nonautonomous General Dynamical SystemsSpringer Science and Business Media LLC - Tập 22 - Trang 117-154 - 2013
Yejuan Wang, Desheng Li
The Morse decomposition theory for nonautonomous general dynamical systems (set-valued dynamical systems) and differential inclusions is established. The stability of Morse decompositions of pullback attractors is also addressed.
Uniqueness for Quasi-variational InequalitiesSpringer Science and Business Media LLC - Tập 24 - Trang 285-297 - 2015
Axel Dreves
This paper presents a uniqueness result for a quasi-variational inequality QVI(1) that, in contrast to existing results, does not require the projection mapping on a variable closed and convex set to be a contraction. Our basic idea is to find a simple QVI(0), for example a variational inequality, for which we can show the existence of a unique solution. Further, exploiting some nonsingularity con...... hiện toàn bộ
Bornological Convergences on the Hyperspace of a Uniformizable SpaceSpringer Science and Business Media LLC - Tập 24 - Trang 597-618 - 2016
Marco Rosa, Paolo Vitolo
Bornological convergence is a generalization of the well known Attouch–Wets convergence. Our aim is to compare lower, upper and “two-sided” convergences generated by two compatible uniformities and two arbitrary bornologies. Moreover, the comparison of convergences induced by bounded-proximal topologies is characterized.
A Remark on the Convergence of the Douglas–Rachford Iteration in a Non-convex SettingSpringer Science and Business Media LLC - Tập 26 - Trang 207-225 - 2018
Ohad Giladi
Using a known construction of a Lyapunov function, it is shown that the Douglas–Rachford iteration with respect to a sphere and a line in a Hilbert space converges to the intersection point in a fashion which is stronger than uniform convergence on compact sets.