Optimality Conditions For Henig And Globally Proper Efficient Solutions And Connectedness Of Their Solution Sets

In this paper, firet of all, we introduce the definitions of Henig subdifferentialand Henig globally subdifferential for set-valued maps. We investigate the existenceconditions for these two kinds of subdifferentials, and discuss their operationalproperties. Using these two concepts, we present the necessary conditions andsufficient conditions for Henig efficient solution pair and Henig globally properefficient solution pair for constrained set-valued vector optimization problems innormed spaces, respectively. Secondly, We obtain the necessary and sufficientconditions for f-efficient solution pair and strong solution pair for the set-valuedvector optimization problem with constraint in locally convex space when theconstraint cones do not necessarily have nonempty topological interiors. Finally, wediscuss the connectedness of the sets of Henig efficient solution and Henig globallyproper efficient solution in locally convex spaces.