Error bounds and metric subregularity

By Alexander Y. Kruger. 2014

123 citations recorded by the source corpus.

Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued functions of two variables. A classification scheme for the general error bound and metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f2d3308815674db6b40d79a3fb9382d878f4dcce

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Alexander Y. Kruger
2. Anthony Man-Cho So
3. Zirui Zhou
4. Asen L. Dontchev

In Computational Theory and Mathematics

1. Alexander Y. Kruger
2. Radek Cibulka
3. Anthony Man-Cho So
4. Zirui Zhou
5. Asen L. Dontchev
6. A. S. Lewis
7. Dmitriy Drusvyatskiy
8. Alexander D. Ioffe

In Geometry and Topology

1. Anthony Man-Cho So
2. Zirui Zhou
3. Alexander Y. Kruger
4. Radek Cibulka
5. Asen L. Dontchev

Citations in the corpus

• A unified approach to error bounds for structured convex optimization problems (2015, background): “…from Before we proceed further, let us briefly illustrate some of the concepts above. and there exist constants κ, ǫ > 0 such that The notions of calmness and metric sub-regularity have played a central role in the study of error bounds; see, e.g. , [26, 9, 31, 27, 15] and the references therein.”
• Strong metric subregularity of mappings in variational analysis and optimization (2017, background): “extensively used in [26] when characterizing metric subregularity.”
• Error Bounds and Hölder Metric Subregularity (2014, methodology): “This allows one to apply to it the extension of the theory of error bounds to functions of two variables developed in [31] and used there for characterizing standard metric subregularity (case q = 1).”