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The sparse form of one of the most successful Variable Metric Methods (BFGS [1, 2]) is used to solve power system optimization problems. The main characteristic of the method is that the sparse factors of the Hessian matrix are used as opposed to a full inverse Hessian. In addition, these factors are updated at every BFGS iteration using a fast and robust sparsity oriented updating algorithm.
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Housos et al. (1982) studied this question.
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