Journal of Global Optimization

, Volume 41, Issue 1, pp 1–13 | Cite as

Lipschitz behavior of convex semi-infinite optimization problems: a variational approach

  • Maria J. Cánovas
  • Abderrahim Hantoute
  • Marco A. López
  • Juan Parra


In this paper we make use of subdifferential calculus and other variational techniques, traced out from [Ioffe, A.D.: Metric regularity and subdifferential calculus. Uspekhi Mat. Nauk 55, 3(333), 103–162; Engligh translation Math. Surveys 55, 501–558 (2000); Ioffe, A.D.: On rubustness of the regularity property of maps. Control cybernet 32, 543–554 (2003)], to derive different expressions for the Lipschitz modulus of the optimal set mapping of canonically perturbed convex semi-infinite optimization problems. In order to apply this background for obtaining the modulus of metric regularity of the associated inverse multifunction, we have to analyze the stable behavior of this inverse mapping. In our semi-infinite framework this analysis entails some specific technical difficulties. We also provide a new expression of a global variational nature for the referred regularity modulus.


Convex semi-infinite programming Metric regularity Optimal set Lipschitz modulus 

Mathematics Subject Classification

90C34 49J53 90C25 90C31 


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Copyright information

© Springer Science+Business Media LLC 2007

Authors and Affiliations

  • Maria J. Cánovas
    • 1
  • Abderrahim Hantoute
    • 1
  • Marco A. López
    • 2
  • Juan Parra
    • 1
  1. 1.Operations Research CenterMiguel Hernández University of ElcheElcheSpain
  2. 2.Department of Statistics and Operations ResearchUniversity of AlicanteAlicanteSpain

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