Fajardo, Maria Dolores, López Cerdá, Marco A., Puente, Rubén
Linear representations and quasipolyhedrality of a finite-valued convex function
FAJARDO GÓMEZ, María Dolores; LÓPEZ CERDÁ, Marco Antonio; PUENTE, Rubén. “Linear representations and quasipolyhedrality of a finite-valued convex function”. Optimization. Vol. 57, Issue 2 (Jan. 2008). ISSN 0233-1934, pp. 215-237
URI: http://hdl.handle.net/10045/8374
DOI: 10.1080/02331930701779864
ISSN: 0233-1934 (Print)
Abstract: 
The possibility of representing the epigraph of a finite-valued convex function by means of a (locally) Farkas-Minkowski linear semi-infinite inequalities system is studied in this article. Moreover, we prove that the so-called locally polyhedral representations characterize the function, giving rise to the concept of quasipolyhedral function. Conditions for its conjugate to be also quasipolyhedral are obtained, as well as the characterization of its subdifferential and eps-subdifferential in terms of an specific sequence of ordinary polyhedral functions.
Keywords:Semi-infinite linear inequality systems, Quasipolyhedral convex sets, Suddifferential set, Conjugate function, Valadier formula
Taylor & Francis
info:eu-repo/semantics/article