## Preprint 2013-26

## Fernando Flores-Bazán, Fabián Flores-Bazán, Sigifredo Laengle:

### Characterizing efficiency on infinite-dimensional commodity spaces with ordering cones having possibly empty interior

### Abstract:

Some production models in a finance economy 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.

This preprint gave rise to the following definitive publication(s):

**Fabián FLORES-BAZáN, Fernando FLORES-BAZáN, Sigifredo LAENGLE: ***Characterizing efficiency on infinite-dimensional commodity spaces with ordering cones having possibly empty interior*. Journal of Optimization Theory and Applications, vol. 164, 2, pp. 455-478, (2015).