Levels Sets Infimal Convolution and Level Addition

D. T. Luc and M. Volle
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D. T. Luc: Université d'Avignon
M. Volle: Université d'Avignon

Journal of Optimization Theory and Applications, 1997, vol. 94, issue 3, No 8, 695-714

Abstract: Abstract A sufficient criterion is established for the infimal convolution of two functions having connected level sets to share the same property without being exact. As a consequence, the infimal convolution of quasiconvex functions on a real line is quasiconvex. However, this is not true on a space of higher dimension, which is illustrated by an example in R 2. Furthermore, connectedness of level sets and local-global minimum properties of functions are analyzed under level addition. Continuity properties of level set maps are also studied in relation with local-global minimum properties.

Keywords: Infimal convolution; level sum; connected level set; quasi-convex function (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022657102069

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