A simplified conjugation scheme for lower semi-continuous functions

Abstract

We present two generalized conjugation schemes for lower semi-continuous functions defined on a real Banach space whose norm is Fréchet differentiable off the origin, and sketch their applications to optimization duality theory. Both approaches are based upon a new characterization of lower semi-continuous functions as pointwise suprema of a special class of continuous functions.

Keywords:

• lower semi-continuous function
• generalized convex conjugation
• optimization duality theory

Acknowledgements

We are grateful to Wilfredo Sosa and two anonymous referees for their valuable comments and suggestions. The author gratefully acknowledges the financial support received from CAPES and the warm hospitality of the second author as well as of the members from the host institution.

Notes

No potential conflict of interest was reported by the authors.

This work was developed during a visit of this author to the Departament d’Economia i d’Història Econòmica of the Universitat Autònoma de Barcelona.

Additional information

Funding

This research was supported by CAPES [grant number BEX 3843/14-9]; MICINN of Spain [grant number MTM2011-29064-C03-01]; Australian Research Council’s Discovery Projects funding scheme [project number DP140103213].