Optimization Letters

, Volume 9, Issue 3, pp 513–521 | Cite as

Boundary of subdifferentials and calmness moduli in linear semi-infinite optimization

  • M. J. Cánovas
  • A. Hantoute
  • J. Parra
  • F. J. Toledo
Original Paper

Abstract

This paper was originally motivated by the problem of providing a point-based formula (only involving the nominal data, and not data in a neighborhood) for estimating the calmness modulus of the optimal set mapping in linear semi-infinite optimization under perturbations of all coefficients. With this aim in mind, the paper establishes as a key tool a basic result on finite-valued convex functions in the \(n\)-dimensional Euclidean space. Specifically, this result provides an upper limit characterization of the boundary of the subdifferential of such a convex function. When applied to the supremum function associated with our constraint system, this characterization allows us to derive an upper estimate for the aimed calmness modulus in linear semi-infinite optimization under the uniqueness of nominal optimal solution.

Keywords

Variational analysis Calmness Semi-infinite programming  Linear programming 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • M. J. Cánovas
    • 1
  • A. Hantoute
    • 2
  • J. Parra
    • 1
  • F. J. Toledo
    • 1
  1. 1.Center of Operations ResearchMiguel Hernández University of ElcheElcheSpain
  2. 2.Departamento de Ingeniería Matemático, Centro de Modelamiento Matemático (CMM)Universidad de ChileSantiagoChile

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