Enhanced Computation of the Proximity Operator for Perspective Functions

In this paper, we provide an explicit expression for the proximity operator of a perspective of any proper lower semicontinuous convex function defined on a Hilbert space. Our computation enhances and generalizes known formulae for the case when the Fenchel conjugate of the convex function has an open domain or when it is radial. We show numerically that our approach is more efficient than previous approaches in the literature and we provide several examples of nonradial functions for which the domain of its conjugate is not open and we compute the proximity operators of their perspectives.