Optimal decomposition for infimal convolution on Banach Couples
2013 (English)Report (Other academic)
Infimal convolution of functions defined on a regular Banach couple is considered. By using a theorem due to Attouch and Brezis, we establish sufficient conditions for this infimal convolution to be subdifferentiable. We also provide a result which gives a dual characterization of optimal decomposition for an infimal convolution in general. We plan tu use these results as tools to study the mathematical properties of exact minimizers for the K–, L–, and E– functionals of the theory of real interpolation. This will be done in a separate study. In this study, we apply our approach to two well–known optimization problems, namely convex and linear programming and provide proofs for duality theorems based on infimal convolution.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. , 23 p.
LiTH-MAT-R, ISSN 0348-2960 ; 7
IdentifiersURN: urn:nbn:se:liu:diva-94152ISRN: LiTH-MAT-R--2013/07--SEOAI: oai:DiVA.org:liu-94152DiVA: diva2:629625