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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
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
Global Solutions for Nonlinear Delay Evolution Inclusions with Nonlocal Initial Conditions
Springer Science and Business Media LLC - - 2012
Ioan I. Vrabie
Sensitivity Analysis of Stochastic Constraint and Variational Systems via Generalized Differentiation
Springer Science and Business Media LLC - Tập 31 - Trang 1-29 - 2023
Boris S. Mordukhovich, Pedro Pérez-Aros
This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian stability and/or metric regularity, of such systems by employing and developing coderivative characterizations of well-posedness properties for random multifun...... hiện toàn bộ
Location, Identification, and Representability of Monotone Operators in Locally Convex Spaces
Springer Science and Business Media LLC - Tập 27 - Trang 151-168 - 2017
M. D. Voisei
In this paper we study, in the relaxed context of locally convex spaces, intrinsic properties of monotone operators needed for the sum conjecture for maximal monotone operators to hold under classical interiority-type domain constraints.
Viability Theorem for Deterministic Mean Field Type Control Systems
Springer Science and Business Media LLC - Tập 26 - Trang 993-1008 - 2018
Yurii Averboukh
A mean field type control system is a dynamical system in the Wasserstein space describing an evolution of a large population of agents with mean-field interaction under a control of a unique decision maker. We develop the viability theorem for the mean field type control system. To this end we introduce a set of tangent elements to the given set of probabilities. Each tangent element is a distrib...... hiện toàn bộ
The Metric Integral of Set-Valued Functions
Springer 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
Localizing Vector Optimization Problems with Application to Welfare Economics
Springer Science and Business Media LLC - Tập 22 - Trang 483-501 - 2013
Amos Uderzo
In the present paper, the Polyak’s principle, concerning convexity of the images of small balls through C1, 1 mappings, is employed in the study of vector optimization problems. This leads to extend to such a context achievements of local programming, an approach to nonlinear optimization, due to B.T. Polyak, which consists in exploiting the benefits of the convex local behaviour of certain noncon...... hiện toàn bộ
Preface
Springer Science and Business Media LLC - Tập 26 - Trang 205-206 - 2018
Heinz H. Bauschke, Boris S. Mordukhovich, Claudia S. Sagastizábal, Michel A. Théra
On Diagonal Subdifferential Operators in Nonreflexive Banach Spaces
Springer Science and Business Media LLC - Tập 20 - Trang 1-14 - 2011
A. N. Iusem, Benar Fux Svaiter
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 ...... hiện toàn bộ
Representative Functions, Variational Convergence and Almost Convexity
Springer 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
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