38 research outputs found
Metric Regularity of the Sum of Multifunctions and Applications
In this work, we use the theory of error bounds to study metric regularity of
the sum of two multifunctions, as well as some important properties of
variational systems. We use an approach based on the metric regularity of
epigraphical multifunctions. Our results subsume some recent results by Durea
and Strugariu.Comment: Submitted to JOTA 37 page
Metric regularity and systems of generalized equations
The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity and metric multi-regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version of Lyusternik-Graves theorem due to Milyutin. The criteria are applied to systems of generalized equations producing some "error bound" type estimates. © 2007 Elsevier Inc. All rights reserved
The Radius of Metric Regularity Revisited
The paper extends the 2003 radius of metric regularity theorem by Dontchev,
Lewis & Rockafellar by providing an exact formula for the radius with respect
to Lipschitz continuous perturbations in general Asplund spaces, thus,
answering affirmatively an open question raised twenty years ago by Ioffe. In
the non-Asplund case, we give natural upper bounds for the radius complementing
the conventional lower bound in the theorem by Dontchev, Lewis & Rockafellar.Comment: 14 page
On Almost Regular Mappings
Ioffe's criterion and various reformulations of it have become a~standard
tool in proving theorems guaranteeing various regularity properties such as
metric regularity, i.e., the openness with a linear rate around the reference
point, of a~(set-valued) mapping. We derive an analogue of it guaranteeing the
almost openness with a linear rate of mappings acting in incomplete spaces and
having non-closed graphs, in general. The main tool used is an approximate
version of Ekeland's variational principle for a function that is not
necessarily lower semi-continuous and is defined on an abstract (possibly
incomplete) space. Further, we focus on the stability of this property under
additive single-valued and set-valued perturbations.Comment: 23 page