Per-se Privacy Preserving Distributed Optimization

Distributed optimization is a fundamental mathematical theory for parallel and distributed systems. Several applications are normally designed based on such a theory, where parties cooperatively exchange messages with little or no central coordination to achieve some goals. In many situations, the transactions among the parties must be private, such as among members of social networks, hospitals, companies in a free market, banks, and state governments, to mention a few. Existing privacy preserving solution methods for optimization problems are mostly based on cryptographic procedures and thus have the drawback substantial computational complexity, which is infeasible for large scale networks. The availability of distributed optimization solution methods that are private per se are therefore highly desirable and sometimes the only ones viable. Surprisingly, little attention has been devoted thus far to the development of a general theory for such privacy preserving distributed optimization. In this survey paper, a new general framework of existing transformation based mechanisms for privacy preserving distributed optimization is presented. The privacy preserving properties that are inherent in the classical decomposition techniques, such as primal decomposition, dual decomposition and stateof-the-art methods, such as alternating direction method of multipliers are investigated. A number of examples is provided to illustrate the need of a new theory of per-se privacy preserving optimization. It is concluded that the theory is still in its infancy and that huge benefits can be achieved by a substantial development.