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This paper presents the Distributed Primal Outer Approximation (DiPOA)algorithm for solving Sparse Convex Programming (SCP) problems with separablestructures, efficiently, and in a decentralized manner. The DiPOA algorithmdevelopment consists of embedding the recently proposed Relaxed HybridAlternating Direction Method of Multipliers (RH-ADMM) algorithm into the OuterApproximation (OA) algorithm. We also propose two main improvements to controlthe quality and the number of cutting planes that approximate nonlinearfunctions. In particular, the RH-ADMM algorithm acts as a distributed numericalengine inside the DiPOA algorithm. DiPOA takes advantage of the multi-corearchitecture of modern processors to speed up optimization algorithms. Theproposed distributed algorithm makes practical the solution of SCP in learningand control problems from the application side. This paper concludes with aperformance analysis of DiPOA for the distributed sparse logistic regressionand quadratically constrained optimization problems. Finally, the paperconcludes with a numerical comparison with state-of-the-art optimizationsolvers.

Distributed Primal Outer Approximation Algorithm for Sparse Convex Programming with Separable Structures