Distributed primal outer approximation algorithm for sparse convex programming with separable structures

Alireza Olama (), Eduardo Camponogara () and Paulo R. C. Mendes ()
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Alireza Olama: Federal University of Santa Catarina
Eduardo Camponogara: Federal University of Santa Catarina
Paulo R. C. Mendes: Fraunhofer Institute for Industrial Mathematics

Journal of Global Optimization, 2023, vol. 86, issue 3, No 5, 637-670

Abstract: Abstract This paper presents the distributed primal outer approximation (DiPOA) algorithm for solving sparse convex programming (SCP) problems with separable structures, efficiently, and in a decentralized manner. The DiPOA algorithm development consists of embedding the recently proposed relaxed hybrid alternating direction method of multipliers (RH-ADMM) algorithm into the outer approximation (OA) algorithm. We also propose two main improvements to control the quality and the number of cutting planes that approximate nonlinear functions. In particular, the RH-ADMM algorithm acts as a distributed numerical engine inside the DiPOA algorithm. DiPOA takes advantage of the multi-core architecture of modern processors to speed up optimization algorithms. The proposed distributed algorithm makes practical the solution of SCP in learning and control problems from the application side. This paper concludes with a performance analysis of DiPOA for the distributed sparse logistic regression and quadratically constrained optimization problems. Finally, the paper concludes with a numerical comparison with state-of-the-art optimization solvers.

Keywords: Outer approximation; Sparse convex programming; Distributed optimization; Message passing interface (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01266-5

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