  Locating proximal points is a component of numerous minimization algorithms.
This work focuses on developing a method to find the proximal point of a convex
function at a point, given an inexact oracle. Our method assumes that exact
function values are at hand, but exact subgradients are either not available or
not useful. We use approximate subgradients to build a model of the objective
function, and prove that the method converges to the true prox-point within
acceptable tolerance. The subgradient $g_k$ used at each step $k$ is such that
the distance from $g_k$ to the true subdifferential of the objective function
at the current iteration point is bounded by some fixed $\varepsilon>0.$ The
algorithm includes a novel tilt-correct step applied to the approximate
subgradient.
