Mass-spring-damper Networks for Distributed Optimization in Non-Euclidean Spaces

2018/08/06 by Yue Yu, Yu, Yue, Behçet Açıkmeşe +3
Computer Science · Engineering · #Distributed Control Multi-Agent Systems #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1808.01999

openalex publication_date 2018/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of minimizing the sum of non-smooth convex functions in non-Euclidean spaces, e.g., probability simplex, via only local computation and communication on an undirected graph. We propose two algorithms motivated by mass-spring-damper dynamics. The first algorithm uses an explicit update that computes subgradients and Bregman projections only, and matches the convergence behavior of centralized mirror descent. The second algorithm uses an implicit update that solves a penalized subproblem at each iteration, and achieves the iteration complexity of \(O(1/K)\). The results are also demonstrated via numerical examples.

Citations

• Constrained Consensus and Optimization in Multi-Agent Networks

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