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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.
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