Arcwise connectedness of closed efficient point sets
One of the most important problems of vector optimization is to investigate the structure of efficient point sets. For various applications, the possibility of continuous moving from one optimal solution to any other along optimal alternatives only is of special interest. This possibility is guaranteed if the efficient set is arcwise connected or at least connected. In this paper the authors prove that the efficient point set \(\text{Max} (Q\mid K)\) of a compact convex set \(Q\subset X\) in a Hausdorff topological vector space \(X\) ordered by a closed convex cone \(K\subset X\) is arcwise connected if the set \(\text{Max} (Q\mid K)\) is closed.
scientific article; zbMATH DE number 1497250