19 research outputs found
On a Sufficient Condition for Weak Sharp Efficiency in Multiobjective Optimization
No full textIn this paper, we provide sufficient conditions entailing the existence of
weak sharp efficient points of a multiobjective optimization problem. The approach
uses variational analysis techniques, like regularity and subregularity of the diagonal
subdifferential map related to a suitable scalar equilibrium problem naturally associated
to the multiobjective optimization problem
On borel probability measures and noncooperative game theory
No full textIn this article, the well-known minimax theorems of Wald, Ville and von Neumann are generalized under weaker topological conditions on the payoff function/and/or extended to the larger set of the Borel probability measures, instead of the set of mixed strategies
An inverse map result and some applications to sensitivity of generalized equations
No full textThis work deals with non–global inverse map results for the sum of two maps. We prove
two theorems which shed some new light on this aspect. Some implications in terms
of sensitivity of parametric generalized equations are investigated. Finally, a class of
well–conditioned operators is identified
Conditioning for optimization problems under general perturbations
No full textGiven a function f in the class C^(1,1)B(0, r), where B(0, r) denotes a ball of radius r in a real Banach
space E, we provide the definition of a positive extended real number c*(f ) defined through
the function, that plays a role in the study of the sensitivity of the Argmin map of the
perturbed function F_g (p, u) = f (u) − g(p, u). This number coincides with the number
c_2(f ) introduced by Zolezzi (2003) if linear perturbations g(p, u) = are considered
Existence of Equilibria via Ekeland's Principle
No full textIn the literature, when dealing with equilibrium problems and the existence of their solutions, the
most used assumptions are the convexity of the domain and the generalized convexity andmonotonicity,
together with some weak continuity assumptions, of the function. In this paper, we focus on
conditions that do not involve any convexity concept, neither for the domain nor for the function
involved. Starting from the well-known Ekeland’s theorem for minimization problems, we find a
suitable set of conditions on the function f that lead to an Ekeland’s variational principle for equilibrium
problems. Via the existence of -solutions, we are able to show existence of equilibria on
general closed sets for equilibrium problems and systems of equilibrium problems
Well-posed vector equilibrium problems
No full textWe introduce and study two notions of well-posedness for vector equilibrium
problems in topological vector spaces; they arise from the well-posedness
concepts previously introduced by the same authors in the scalar case, and provide
an extension of similar definitions for vector optimization problems. The first notion
is linked to the behaviour of suitable maximizing sequences, while the second one is
defined in terms of Hausdorff convergence of the map of approximate solutions. In
this paper we compare them, and, in a concave setting, we give sufficient conditions
on the data in order to guarantee well-posedness. Our results extend similar results
established for vector optimization problems known in the literature
Well-posed equilibrium problems
No full textIn this paper we introduce some notions of well-posedness for scalar equilibrium problems
in complete metric spaces or in Banach spaces. As equilibrium problem is a common
extension of optimization, saddle point and variational inequality problems, our definitions
originates from the well-posedness concepts already introduced for these problems.
We give sufficient conditions for two different kinds of well-posedness and show
by means of counterexamples that these have no relationship in the general case.
However, together with some additional assumptions, we show via Ekeland's principle for
bifunctions a link between them.
Finally we discuss a parametric form of the equilibrium problem and introduce a
well-posedness concept for it, which unifies the two different notions of well-posedness
introduced in the first part
Linear openness of the composition of set-valued maps and applications to variational systems
No full textIn this paper we study the linear openness of the composition of set-valued maps carried out thanks to applications of Nadler's fixed point theorem and Lim's lemma.
As a byproduct, we obtain the Lipschitz property of the solution map of a generalized parametric equation and of parametric approximate variational inequalities, as well
Ekeland's principle for vector equilibrium problem
No full textIn this paper, the authors deal with bifunctions defined on complete metric spaces and with values in
locally convex spaces ordered by closed convex cones. The aim is to provide a vector version of Ekeland’s
theorem related to equilibrium problems. To prove this principle, a weak notion of continuity of a vectorvalued
function is considered, and some of its properties are presented. Via the vector Ekeland’s principle,
existence results for vector equilibria are proved in both compact and noncompact domains
Stability Results of Variational Systems Under Openness with Respect to Fixed Sets
No full textIn this paper we present the notions of (U; V )-openness and (U; V )-
metric regularity for a set-valued map, proving their equivalence. By using
different approaches we show the stability, with respect to the sum of maps,
of the (U; V )-openness property, both in the setting of Banach spaces, and of
metric spaces. Finally, we infer the regularity of the map solving a generalized
parametric equation defined via a parametric map that is, in its turn,
perturbed by the sum with another map
