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

TL;DR

This paper introduces DiPOA, a distributed algorithm combining outer approximation and RH-ADMM for efficiently solving sparse convex programming problems with separable structures, leveraging multi-core architectures.

Contribution

The paper develops a novel distributed primal outer approximation algorithm that integrates RH-ADMM, improving control over the approximation quality and enabling scalable solutions for sparse convex problems.

Findings

DiPOA effectively solves distributed sparse logistic regression.

DiPOA outperforms traditional solvers in computational efficiency.

The method is suitable for learning and control applications with separable structures.

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.