Characterizations of nonemptiness and compactness of the set of weakly efficient solutions for convex vector optimization and applications

In this paper, we give characterizations for the nonemptiness and compactness of the set of weakly efficient solutions of an unconstrained/constrained convex vector optimization problem with extended vector-valued functions in terms of the 0-coercivity of some scalar functions. Finally, we apply these results to discuss solution characterizations of a constrained convex vector optimization problem in terms of solutions of a sequence of unconstrained vector optimization problems which are constructed with a general nonlinear Lagrangian.