Abstract
We describe a variational principle based upon minimizing the extent to which the inverse hessian approximation, sayH, violates the quasi-Newton relation, on the step immediately prior to the step used to constructH. Its application to the case when line searches are exact suggests use of the BFGS update.
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This paper is based upon results first presented at the 1979 Mathematical Programming Symposium. Montreal, Canada.
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Nazareth, L. An alternative variational principle for variable metric updating. Mathematical Programming 30, 99–104 (1984). https://doi.org/10.1007/BF02591801
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DOI: https://doi.org/10.1007/BF02591801