Abstract

We introduce two notions of vector asymptotic functions for vector functions with their image space ordered by the nonnegative orthant. To do this, a suitable extended-valued framework is used. We establish properties and formulas for these notions. The asymptotic notions are used to study multiobjective optimization problems. We obtain (outer/inner) estimates for the asymptotic and recession cones of level, colevel, and weakly efficient solution sets. With this information, we establish coercivity properties, coercive and noncoercive existence results for solutions of multiobjective optimization problems.