An epi-convergence result for bivariate convex functions

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1 Scopus citations


We prove that for a large class of convex and lower semi-continuous biavariate functions defined over RN, epi-convergence in one variable implies epi-convergence in both variables. We also show that for closed-valued and graph-convex mappings with domains with non empty interiors, pointwise convergence implies graph convergence. We provide a number of applications for both results.

Original languageEnglish
Pages (from-to)197-208
Number of pages12
JournalJournal of Convex Analysis
Issue number1
StatePublished - 2004


  • Convex functions
  • Differential inclusions
  • Epi-convergence
  • Graph convergence
  • Graph-convex mappings
  • Parametric optimization

ASJC Scopus subject areas

  • Analysis
  • General Mathematics


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