Distributed nested decomposition of staircase linear programs

Abstract

This article considers the application of a primal nested-decomposition method to solve staircase linear programs (SLPs) on distributed-memory, multiple-instruction-multiple-data computers. Due to the coupling that exists among the stages of an SLP, a standard parallel-decomposition algorithm for these problems would allow only a subset of the subproblem processes to overlap with one another at any give time. We propose algorithms that seek to increase the amount of overlap among the processes as well as utilize idle time beneficially. Computational results testing the effectiveness of our algorithms are reported, using a standard set of test problems.

Stackelberg Security Games: Models, Applications and Computational Aspects

“…In addition a lot of new methods were developed recently, from among them: relaxation method [22], Dantzig-Wolfe decomposition [23], primal nested-decomposition method [24].…”

Optimal Agent Cooperation with Local Information

“…For staircase LPs, efficient distributed algorithms based on nested decomposition have been developed (see [40,41] and references therein). In our problem, the optimal value function at separation s ≥ 2 depends on the optimal value function at lower and greater separations (namely, at separations s + σ, for σ = −2, .…”