2025/05/20 by Peter Barkley, Barkley, Peter, Robert L. Bassett +1 · 1 citation
Computer Science · Mathematics · #49M37 #65K05 #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2505.13927
openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a novel matrix-parametrized frugal splitting algorithm which finds the zero of a sum of maximal monotone and cocoercive operators composed with linear selection operators. We also develop a semidefinite programming framework for selecting matrix parameters and demonstrate its use for designing matrix parameters which provide beneficial diagonal scaling, allow parallelization, and adhere to a given communication structure. We show that taking advantage of the linear selection operators in this way accelerates convergence in numerical experiments, and show that even when the selection operators are the identity, we can accelerate convergence by using the matrix parameters to provide appropriately chosen diagonal scaling. We conclude by demonstrating the applicability of this algorithm to multi-stage stochastic programming, outlining a decentralized approach to the relaxed stochastic weapon target assignment problem which splits over the source nodes and has low data transfer and memory requirements.