Article ID: | iaor20041884 |
Country: | India |
Volume: | 40 |
Issue: | 1 |
Start Page Number: | 52 |
End Page Number: | 61 |
Publication Date: | Mar 2003 |
Journal: | OPSEARCH |
Authors: | Lalitha C.S., Davar Sonia |
Keywords: | programming: mathematical |
In this paper we first introduce a class of set-valued quasiconvex maps with respect to cones, called cone quasiconvex maps, and obtain a characterization for cone quasiconvexity at a point in terms of star shapedness. We then introduce a general class of set-valued maps, called weak cone quasiconvex maps and discuss the relations of both these classes of maps with directional derivatives studied by Yang. A sufficient optimality criterion is also established for a set-valued minimization problem assuming the map involved to be cone quasiconvex (weak cone quasiconvex).