Journal of Optimization Theory and Applications

, Volume 95, Issue 3, pp 717-722

First online:

Characterization of R-Evenly Quasiconvex Functions

  • J. E. Martínez-LegazAffiliated withDepartament d'Economia i d'Història Económica and CODE, Universitat Autònoma de Barcelona

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A function defined on a locally convex space is called evenly quasiconvex if its level sets are intersections of families of open half-spaces. Furthermore, if the closures of these open halfspaces do not contain the origin, then the function is called R-evenly quasiconvex. In this note, R-evenly quasiconvex functions are characterized as those evenly-quasiconvex functions that satisfy a certain simple relation with their lower semicontinuous hulls.

Quasiconvex functions duality generalized conjugation