Abstract

We show that the minimization problem of any non-convex and non-lower semi-continuous function on a compact convex subset of a locally convex real topological vector space can be studied via an associated convex and lower semi-continuous function Γ(h). This observation uses the notion of Γ-regularization as a key ingredient. As an application we obtain, on any locally convex real space, a generalization of the Lanford III–Robinson theorem which has only been proven for separable real Banach spaces. The latter is a characterization of subdifferentials of convex continuous functions.

Author information

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

Jean-Bernard Bru

Dep. de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
and: IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain

jeanbernard_bru@ehu.es

Keywords

  • Variational problems
  • non-linear analysis
  • non-convexity
  • Gamma-regularization
  • Lanford III – Robinson theorem

Mathematics Subject Classification

58E30, 46N10, 52A07

References

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Suggested citation

J.-B. Bru, W. de Siqueira Pedra. “Remarks on the Γ–regularization of Non-convex and Non-semi-continuous Functions on Topological Vector Spaces.” Journal of Convex Analysis 19 (2012), No. 2, 467–483. https://doi.org/10.68381/jca19025

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press LLC.