Abstract
In this paper sufficient conditions for local and superlinear convergence to a Kuhn—Tucker point are established for a class of algorithms which may be broadly defined and comprise a quadratic programming algorithm for repeated solution of a subproblem and a variable metric update to develop the Hessian in the subproblem. In particular the DFP update and an update attributed to Powell are shown to provide a superlinear convergent subclass of algorithms provided a start is made sufficiently close to the solution and the initial Hessian in the subproblem is sufficiently close to the Hessian of the Lagrangian at this point.
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This research was supported in part by the National Science Foundation under Grants ENG 75-10486 and GJ 35292.
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Han, SP. Superlinearly convergent variable metric algorithms for general nonlinear programming problems. Mathematical Programming 11, 263–282 (1976). https://doi.org/10.1007/BF01580395
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DOI: https://doi.org/10.1007/BF01580395