Nguyen Duy Cuong ; Alexander Y. Kruger - Uniform Regularity of Set-Valued Mappings and Stability of Implicit Multifunctions

jnsao:6599 - Journal of Nonsmooth Analysis and Optimization, June 22, 2021, Volume 2 - https://doi.org/10.46298/jnsao-2021-6599
Uniform Regularity of Set-Valued Mappings and Stability of Implicit MultifunctionsArticle

Authors: Nguyen Duy Cuong ; Alexander Y. Kruger

    We propose a unifying general (i.e. not assuming the mapping to have any particular structure) view on the theory of regularity and clarify the relationships between the existing primal and dual quantitative sufficient and necessary conditions including their hierarchy. We expose the typical sequence of regularity assertions, often hidden in the proofs, and the roles of the assumptions involved in the assertions, in particular, on the underlying space: general metric, normed, Banach or Asplund. As a consequence, we formulate primal and dual conditions for the stability properties of solution mappings to inclusions


    Volume: Volume 2
    Section: Original research articles
    Published on: June 22, 2021
    Accepted on: June 15, 2021
    Submitted on: June 25, 2020
    Keywords: Mathematics - Optimization and Control
    Funding:
      Source : OpenAIRE Graph
    • Discovery Projects - Grant ID: DP160100854; Funder: Australian Research Council (ARC); Code: DP160100854

    Consultation statistics

    This page has been seen 358 times.
    This article's PDF has been downloaded 239 times.