Vector Optimization Problem Weakly Efficient Solution Of The Set Of Nonempty Bounded Characterizations Of Its Application

We first characterize the nonemptiness and compactness of the weakly efficient solution set of a cone-constrained convex vector optimization problem in a finite-dimensional space when the objective space is ordered by some nontrivial polyhedral cone,and apply the characterizations to the convergence analysis of a class of penalty methods.Then,we characterize the nonemptiness and bound(?)dness of the weakly efficient solution set of a cone-constrained convex vector optimization problem in an infinite-dimensional reflexive Banach space.We also apply the characterizations to the convergence analysis of a class of penalty methods.Furthermore,we will consider the convex vector optimization problem when the objective space R~m is ordered by a nontrivial,polyhedral cone with nonempty interior instead of the nonnegative orthant R_+~m Also,we will characterize the nonemptiness and boundedness of the weakly efficient solution set of the above convex vector optimization problem,especially,a cone-constrained convex vector optimization problem in infinite-dimensional real reflexive Banach spaces.Moreover,we will apply the characterizations to the convergence analysis of a class of penalty methods.