Atsushi Nitanda

Learn More
We now prove the Proposition 1 that gives the condition of compactness of sublevel set. Proof. Let B d (r) and S d−1 (r) denote the ball and sphere of radius r, centered at the origin. By affine transformation, we can assume that X * contains the origin O, X * ⊂ B d (1), and X * ∩ S d−1 (1) = φ. Then, we have that for ∀x ∈ S d−1 (1), (∇f (x), x) ≥ f (x) − f(More)
  • 1