Abstract

We prove that for a large class of convex and lower semi-continuous biavariate functions defined over RN\mathbb{R}^N, 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

Author information

Contact details are reproduced from the original publication and may be historical.

Adib Bagh

Dept. of Economics, University of California, One Shields Avenue, Davis, CA 95616, U.S.A.

bagh@math.ucdavis.edu

Keywords

  • Convex functions
  • graph-convex mappings
  • epi-convergence
  • graph convergence
  • differential inclusions
  • parametric optimization

References

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Suggested citation

Adib Bagh. “An Epi-Convergence Result for Bivariate Convex Functions.” Journal of Convex Analysis 11 (2004), No. 1, 197–208. https://doi.org/10.68381/jca11013

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Published by Heldermann Verlag, 2004. Rights now held by Banach Press LLC.