Artículo de revista
Characterizing Efficiency on Infinite-dimensional Commodity Spaces with Ordering Cones Having Possibly Empty Interior
Fecha
2015Registro en:
J Optim Theory Appl (2015) 164:455–478
DOI 10.1007/s10957-014-0558-y
Autor
Flores Bazán, Fabián
Flores Bazán, Fernando
Laengle Scarlazetta, Sigifredo
Institución
Resumen
Some production models in finance require infinite-dimensional commodity
spaces, where efficiency is defined in terms of an ordering cone having possibly
empty interior. Since weak efficiency is more tractable than efficiency from a
mathematical point of view, this paper characterizes the equality between efficiency
and weak efficiency in infinite-dimensional spaces without further assumptions, like
closedness or free disposability. This is obtained as an application of our main result
that characterizes the solutions to a unified vector optimization problem in terms of
its scalarization. Standard models as efficiency, weak efficiency (defined in terms of
quasi-relative interior), weak strict efficiency, strict efficiency, or strong solutions are
carefully described. In addition, we exhibit two particular instances and compute the
efficient and weak efficient solution set in Lebesgue spaces.