Surrogate methods for linear inequalities
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Three algorithms are developed and validated for finding a pointx inR n that satisfies a given system of inequalities,Ax≤b. A andb are a given matrix and a given vector inR m×n andR m , respectively, with the rows ofA assumed normalized. The algorithms are iterative and are based upon the orthogonal projection of an infeasible point onto the manifold of the bounding hyperplanes of some of the given constraints. The choice of the active constraints and the actual projection are accomplished through the use of surrogate constraints.
Key WordsSurrogate constraints hyperplanes halfspaces orthogonal projections manifolds active constraints linear combinations outward normals
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