  The privacy funnel (PF) gives a framework of privacy-preserving data release,
where the goal is to release useful data while also limiting the exposure of
associated sensitive information. This framework has garnered significant
interest due to its broad applications in characterization of the
privacy-utility tradeoff. Hence, there is a strong motivation to develop
numerical methods with high precision and theoretical convergence guarantees.
In this paper, we propose a novel relaxation variant based on Jensen's
inequality of the objective function for the computation of the PF problem.
This model is proved to be equivalent to the original in terms of optimal
solutions and optimal values. Based on our proposed model, we develop an
accurate algorithm which only involves closed-form iterations. The convergence
of our algorithm is theoretically guaranteed through descent estimation and
Pinsker's inequality. Numerical results demonstrate the effectiveness of our
proposed algorithm.
