Open AccessIll-Posedness of sublinear minimization problems
Author(s) -
Samar Issa,
Mustapha Jazar,
Abdallah El Hamidi
Publication year - 2011
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2011.09.004
Subject(s) - sublinear function , regularization (linguistics) , mathematics , sobolev space , bounded function , bounded variation , minification , pure mathematics , mathematical analysis , mathematical optimization , computer science , artificial intelligence
It is well known that minimization problems involving sublinear regularization terms are ill-posed, in Sobolev spaces. Extended results to spaces of bounded variation functions BV were recently showed in the special case of bounded regularization terms. In this note, a generalization to sublinear regularization is presented in BV spaces. Notice that our results are optimal in the sense that linear regularization leads to well-posed minimization problems in BV spaces