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Capra-Convexity, Convex Factorization and Variational Formulations for the ℓ0 Pseudonorm
Springer Science and Business Media LLC - Tập 30 - Trang 597-619 - 2021
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......
Global Solutions for Nonlinear Delay Evolution Inclusions with Nonlocal Initial Conditions
Springer Science and Business Media LLC - - 2012
The Metric Integral of Set-Valued Functions
Springer Science and Business Media LLC - Tập 26 - Trang 867-885 - 2017
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 ......
On Diagonal Subdifferential Operators in Nonreflexive Banach Spaces
Springer Science and Business Media LLC - Tập 20 - Trang 1-14 - 2011
Consider a real-valued bifunction f defined on C ×C, where C is a closed and convex subset of a Banach space X, which is concave in its first argument and convex in its second one. We study its subdifferential with respect to the second argument, evaluated at pairs of the form (x,x), and the subdifferential of − f with respect to its first argument, evaluated at the same pairs. We prove that if f ......
Representative Functions, Variational Convergence and Almost Convexity
Springer Science and Business Media LLC - Tập 32 - Trang 1-45 - 2024
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......
Morse Decompositions for Nonautonomous General Dynamical Systems
Springer Science and Business Media LLC - Tập 22 - Trang 117-154 - 2013
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.
Single-Directional Properties of Quasi-Monotone Operators
Springer Science and Business Media LLC - Tập 21 - Trang 617-626 - 2013
A large supply of quasi-monotone multivalued mappings with values in a weak* fragmentable dual Banach space is shown to be generically single-directional. This is of some interest in analysis of quasi-convex functions. The paper extends/strengthens some results of a recent paper by Aussel and Eberhard (Math Program 30, 2012).
Uniqueness for Quasi-variational Inequalities
Springer Science and Business Media LLC - Tập 24 - Trang 285-297 - 2015
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......
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