2020/03/03 by Bruce Cox, Cox, Bruce A.
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2003.01562
openalex publication_date 2020/03/03 · openalex created_date 2020/03/13 · openalex updated_date 2026/07/28
Several well known large scale linear programming decomposition methodologies exist. Benders Decomposition, which covers the case where some small subset of variables link the otherwise separable subproblems. Dantzig-Wolfe decomposition and Lagrangian decompositions, which cover the case where some few constraints link the otherwise separable subproblems, and finally the "Cross-Decomposition" originating from TJ Van Roy which enables one to deal with both linking constraints and linking variables by essentially alternating iteratively between the Benders and the Lagrangian Decomposition. In this paper we present a novel alternative to Cross-decomposition that deals with both linking constraints and linking variables through the application of accuracy certificates for black-box, sub-gradient based algorithms such as NERML.