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

Computing proximal points of convex functions with inexact subgradients