Subdifferential calculus rules in convex analysis: A unifying approach via pointwise supremum functions

Hantoute, A.; López, M.A.

Keywords: convex analysis, convex subdifferential, pointwise supremum function, calculus rules

Abstract

We provide a rule to calculate the subdifferential set of the pointwise supremum of an arbitrary family of convex functions defined on a real locally convex topological vector space. Our formula is given exclusively in terms of the data functions and does not require any assumption either on the index set on which the supremum is taken or on the involved functions. Some other calculus rules, namely chain rule formulas of standard type, are obtained from our main result via new and direct proofs.

Más información

Título de la Revista: SIAM JOURNAL ON OPTIMIZATION
Volumen: 19
Número: 2
Editorial: SIAM PUBLICATIONS
Fecha de publicación: 2008
Página de inicio: 863
Página final: 882
Idioma: English
Financiamiento/Sponsor: Research supported by grants MTM2005-08572- C03 (01) from MEC (Spain) and FEDER (E.U.), ACOMP06/117 and ACOMP/2007/247-292 from Generalitat Valenciana (Spain), and ID-PCE-379 (Romania)
DOI:

DOI. 10.1137/070700413

Notas: ISI