Existence and Boundedness of Solutions in Infinite-Dimensional Vector Optimization Problems
This work focuses on the nonemptiness and boundedness of the sets of efficient and weak efficient solutions of a vector optimization problem, where the decision space is a normed space and the image space is a locally convex Hausdorff topological linear space. By studying certain boundedness and coercivity concepts of vector-valued functions and via an asymptotic analysis, we extend to this kind of problems some well-known existence and boundedness results for efficient and weak efficient solutions of multiobjective optimization problems with Pareto or polyhedral orderings. Some of these results are proved under weaker assumptions.
boundedness weak efficient solution efficient solution coercivity convex vector optimization existence theorems asymptotic function asymptotic cone linear scalarization domination property 49j27 90c29