A parallel relaxation method for quadratic programming problems with interval constraints

Abstract

Optimization problems with interval constraints are encountered in various fields such as network flows and computer tomography. As these problems are usually very large, they are not easy to solve without taking their sparsity into account. Recently “row-action methods”, which originate from the classical Hildreth's method for quadratic programming problems, have drawn much attention, since they are particularly useful for large and sparse problems. Various row-action methods have already been proposed for optimization problems with interval constraints, but they mostly belong to the class of sequential methods based on the Gauss-Seidel and SOR methods. In this paper, we propose a highly parallelizable method for solving those problems, which may be regarded as an application of the Jacobi method to the dual of the original problems. We prove convergence of the algorithm and report some computational results to demonstrate its effectiveness.