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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
Sensitivity Analysis of Stochastic Constraint and Variational Systems via Generalized Differentiation
Springer Science and Business Media LLC - Tập 31 - Trang 1-29 - 2023
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...
Location, Identification, and Representability of Monotone Operators in Locally Convex Spaces
Springer Science and Business Media LLC - Tập 27 - Trang 151-168 - 2017
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
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...
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 to consist of integrals of all the metric selections of the
integrated multifunction. The metric integral is a subset of the Aumann
integral, but in cont...
Localizing Vector Optimization Problems with Application to Welfare Economics
Springer Science and Business Media LLC - Tập 22 - Trang 483-501 - 2013
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...
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...
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