Applied Mathematics Colloquium: Dr. Goran Lesaja

Title: A Second Order Cone Formulation of Continuous Control Tabular Adjustment Model

In this talk   a minimum distance Controlled Tabular Adjustment (CTA) model for statistical disclosure limitation (control) of tabular data is considered. The goal of the CTA model is to find the closest safe table to some original tabular data set that contains sensitive information. The measure of closeness is usually measured using $\ell_1$ or  $\ell_2$ norm; with each measure having its advantages and disadvantages. Recently,  a regularization of the $\ell_1$-CTA using Pseudo-Huber function was introduced in an attempt to combine positive characteristics of both $\ell_1$-CTA and $\ell_2$-CTA. All three models  can  be solved using appropriate versions of Interior-Point Methods (IPM). It is known that IPM in general  works better on well structured problems such as conic optimization problems, thus, reformulation of these CTA models as conic optimization problem may be advantageous. We present reformulation of Pseudo-Huber-CTA, and $\ell_1$-CTA as Second-Order Cone (SOC) optimization problems and  present preliminary, initial numerical tests showing the validity of the approach on the small set of two-dimensional tables.