Set intersection theorems and existence of optimal solutions
In this interesting paper one establishes sufficient conditions for a decreasing sequence of closed subsets of \(\mathbb{R}^{n}\) to have nonempty intersection. The conditions are formulated in terms of asymptotic directions, retractive directions and horizon directions. In order to apply the results to the existence of global solutions for constrained minimization problems one introduces the notion of bidirectionally flat convex functions. One recovers so the Frank-Wolfe theorem.
scientific article; zbMATH DE number 5151338
scientific article