Download Variable Metric Relaxation Methods, Part I: a Conceptual Algorithm Pdf

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By:Stanford University. Department of Operations Research. Systems Optimization Laboratory,Jean-Louis Goffin
Published on 1981 by


A variable metric, maximal ellipsoidal distance, relaxation method for solving systems of linear, inequalities is described and its rate of convergence analyzed. This algorithm, with a termination routine appended to it, is polynomial if the ellipsoid matrix approximates an inverse 'Hessian, ' which may be defined through the largest ellipsoid contained in a perturbation cum compactification of the feasible set. This so called inverse Hessian is given by a positive linear combination of symmetric rank one matrices built on the vectors given by the facets of the perturbation cum compactification of the feasible set. (Author).

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