Perspective Reformulations of the CTA Problem with <i>L</i>₂ Distances

作     者：Castro, Jordi Frangioni, Antonio Gentile, Claudio 

作者机构：Univ Politecn Cataluna Dept Stat & Operat Res ES-08034 Barcelona Catalonia Spain Univ Pisa Dipartimento Informat I-56127 Pisa Italy CNR Ist Anal Sistemi & Informat I-00185 Rome Italy 

出 版 物：《OPERATIONS RESEARCH》 (运筹学)

年 卷 期：2014年第62卷第4期

页      面：891-909页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Spanish Ministry of Economy and Competitiveness [MTM2012-31440] Government of Catalonia [SGR-2009-1122] Mixed-Integer Nonlinear Optimization: Approaches and Applications Italian Ministry of Education, University and Research [2012JXB3YF] Italian National Research Council 

主　　题：mixed integer quadratic programming perspective reformulation data privacy statistical disclosure control tabular data protection controlled tabular adjustment 

摘      要：Any institution that disseminates data in aggregated form has the duty to ensure that individual confidential information is not disclosed, either by not releasing data or by perturbing the released data while maintaining data utility. Controlled tabular adjustment (CTA) is a promising technique of the second type where a protected table that is close to the original one in some chosen distance is constructed. The choice of the specific distance shows a trade-off: although the Euclidean distance has been shown (and is confirmed here) to produce tables with greater utility, it gives rise to mixed integer quadratic problems (MIQPs) with pairs of linked semi-continuous variables that are more difficult to solve than the mixed integer linear problems corresponding to linear norms. We provide a novel analysis of perspective reformulations (PRs) for this special structure;in particular, we devise a projected PR ((PR)-R-2), which is piecewise-conic but simplifies to a (nonseparable) MIQP when the instance is symmetric. We then compare different formulations of the CTA problem, showing that the ones based on (PR)-R-2 most often obtain better computational results.