Surrogate Constraint Methods for Linear Inequalities

Systems of linear inequalities and equations are very important in optimization. Recent applications of mathematical programming in areas such as computerized tomography (CAT scan) lead to very large and sparse systems of linear equations and inequalities which need to be solved approximately within reasonable time. Traditional Phase I linear programming approaches are not appropriate for these problems because of the very large size of the systems and irregular sparsity structure. Iterative relaxation methods can be used to solve these problems, but they tend to be too slow.

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