Solution uniqueness of convex optimization problems via the radial cone

Abstract

In this paper, we mainly study solution uniqueness of some convex optimization problems. Our characterizations of solution uniqueness are in terms of the radial cone. This approach allows us to know when a unique solution is a strong solution or even a tilt-stable one without checking second-order information. Consequently, we apply our theory to low-rank optimization problems. The radial cone is fully calculated in this case and numerical experiments show that our characterizations are sharp.