New contraction methods for linear inequalities (Q1334912)

The author presents a new iterative contraction algorithm of Uzawa type for solving linear inequalities and proves its global linear convergence under the assumption that the solution set is nonempty. The new step- length rule allows to take the step up to 4 times as long as that for the Uzawa method, and the resulting algorithm terminates for systems which have full-dimensional solution set. The numerical results indicate that the new method converges much faster than the original Uzawa method.