Obtaining analogous equality characterizations for simple explicit constraint sets (balls or boxes)

Establish equality characterizations of value-function classes, analogous to those obtained with convex, compact, semi-algebraic lower-level constraints, for simple explicit lower-level constraint sets such as Euclidean balls or boxes, or show that such equalities cannot hold.

Background

After presenting equality characterizations under general convex, compact, semi-algebraic constraints, the authors point out that the resulting feasible sets lack explicit descriptions and mention interest in whether similar, tight results can be achieved for simpler explicit sets.

They specifically mention balls and boxes as target constraint sets for obtaining comparable representation results.