80 research outputs found
H\"older Error Bounds and H\"older Calmness with Applications to Convex Semi-Infinite Optimization
Using techniques of variational analysis, necessary and sufficient
subdifferential conditions for H\"older error bounds are investigated and some
new estimates for the corresponding modulus are obtained. As an application, we
consider the setting of convex semi-infinite optimization and give a
characterization of the H\"older calmness of the argmin mapping in terms of the
level set mapping (with respect to the objective function) and a special
supremum function. We also estimate the H\"older calmness modulus of the argmin
mapping in the framework of linear programming.Comment: 25 page
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
Error bounds revisited
We propose a unifying general framework of quantitative primal and dual sufficient and necessary error bound conditions covering linear and nonlinear, local and global settings. The function is not assumed to possess any particular structure apart from the standard assumptions of lower semicontinuity in the case of sufficient conditions and (in some cases) convexity in the case of necessary conditions. We expose the roles of the assumptions involved in the error bound assertions, in particular, on the underlying space: general metric, normed, Banach or Asplund. Employing special collections of slope operators, we introduce a succinct form of sufficient error bound conditions, which allows one to combine in a single statement several different assertions: nonlocal and local primal space conditions in complete metric spaces, and subdifferential conditions in Banach and Asplund spaces. © 2022 Informa UK Limited, trading as Taylor & Francis Group
About [q]-regularity properties of collections of sets
We examine three primal space local Hoelder type regularity properties of
finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and
uniform [q]-regularity as well as their quantitative characterizations.
Equivalent metric characterizations of the three mentioned regularity
properties as well as a sufficient condition of [q]-subregularity in terms of
Frechet normals are established. The relationships between [q]-regularity
properties of collections of sets and the corresponding regularity properties
of set-valued mappings are discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1309.700
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