We study the optimization problem of finding closed convex sets Γ ⊆ Rdcontaining the origin that minimizeF(Γ) = ∑i=1k wi |θi/2 - pΓ(θi)| 2, where w1, ..., wk 0, θ1, ..., θk in Rd are given, and pΓ(θi) are the closest points in Γ to θi, i = 1, ..., k. This problem is motivated by...