2,834 research outputs found
Set optimization - a rather short introduction
Recent developments in set optimization are surveyed and extended including
various set relations as well as fundamental constructions of a convex analysis
for set- and vector-valued functions, and duality for set optimization
problems. Extensive sections with bibliographical comments summarize the state
of the art. Applications to vector optimization and financial risk measures are
discussed along with algorithmic approaches to set optimization problems
The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour
The resort to utility-theoretical issues will permit us to propose a constructive procedure for deriving a homogeneous of degree one, continuous function that gives raise to a primitive demand function under suitably mild conditions. This constitutes the first elementary proof of a necessary and sufficient condition for an integrability problem to have a solution by continuous (subjective utility) functions. Such achievement reinforces the relevance of a technique that was succesfully formalized in Alcantud and RodrĂguez-Palmero (2001). The analysis of these two works exposes deep relationships between two apparently separate fields: mathematical utility theory and the revealed preference approach to the integrability problem.Strong Axiom of Homothetic Revelation; revealed preference; continuous homogeneous of degree one utility; integrability of demand.
Isotonies on ordered cones throught the concept of a decreasing scale
Using techniques based on decreasing scales, necessary and sufficient conditions are presented for the
existence of a continuous and homogeneous of degree one real-valued function representing a (not necessarily
complete) preorder defined on a cone of a real vector space. Applications to measure theory and expected
utility are given as consequences
The convex real projective orbifolds with radial or totally geodesic ends: a survey of some partial results
A real projective orbifold has a radial end if a neighborhood of the end is
foliated by projective geodesics that develop into geodesics ending at a common
point. It has a totally geodesic end if the end can be completed to have the
totally geodesic boundary.
The purpose of this paper is to announce some partial results. A real
projective structure sometimes admits deformations to parameters of real
projective structures. We will prove a homeomorphism between the deformation
space of convex real projective structures on an orbifold with
radial or totally geodesic ends with various conditions with the union of open
subspaces of strata of the corresponding subset of Lastly, we will talk about the
openness and closedness of the properly (resp. strictly) convex real projective
structures on a class of orbifold with generalized admissible ends.Comment: 36 pages, 2 figure. Corrected a few mistakes including the condition
(NA) on page 22, arXiv admin note: text overlap with arXiv:1011.106
Discrete isometry groups of symmetric spaces
This survey is based on a series of lectures that we gave at MSRI in Spring
2015 and on a series of papers, mostly written jointly with Joan Porti. Our
goal here is to:
1. Describe a class of discrete subgroups of higher rank
semisimple Lie groups, which exhibit some "rank 1 behavior".
2. Give different characterizations of the subclass of Anosov subgroups,
which generalize convex-cocompact subgroups of rank 1 Lie groups, in terms of
various equivalent dynamical and geometric properties (such as asymptotically
embedded, RCA, Morse, URU).
3. Discuss the topological dynamics of discrete subgroups on flag
manifolds associated to and Finsler compactifications of associated
symmetric spaces . Find domains of proper discontinuity and use them to
construct natural bordifications and compactifications of the locally symmetric
spaces .Comment: 77 page
Conditions for the Upper Semicontinuous Representability of Preferences with Nontransitive Indifference
We present different conditions for the existence of a pair of upper semicontinuous functions representing an interval order on a topological space without imposing any restrictive assumptions neither on the topological space nor on the representing functions. The particular case of
second countable topological spaces, which is particularly interesting and frequent in economics,
is carefully considered. Some final considerations concerning semiorders finish the paper
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