Serial and parallel successive overrelaxatíon (SOR) methods are proposed for the solution of the augmented Lagrangian formulation of the dual of a linear program. With the proposed serial version of the method we have solved linear programs with as many as 125,000 constraints and 500,000 variables in less than 72 hours on a MicroVax Il. A, parallel implementation of the method was carried out on a Sequent Balance 21000 multiprocessor with speedup efiiciency of over 65% for problem sizes of up to 10,000 constraints, 40,000 variables and 1,400,000 nonzero matrix elements.
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