Open AccessOptimal conditioning in the convex class of rank two updates
Author(s) -
Robert B. Schnabel
Publication year - 1978
Publication title -
mathematical programming
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.358
H-Index - 131
eISSN - 1436-4646
pISSN - 0025-5610
DOI - 10.1007/bf01609030
Subject(s) - hessian matrix , rank (graph theory) , broyden–fletcher–goldfarb–shanno algorithm , mathematics , conditioning , class (philosophy) , inverse , bounded function , regular polygon , mathematical optimization , convex optimization , combinatorics , computer science , artificial intelligence , statistics , mathematical analysis , computer network , geometry , asynchronous communication
Davidon's new quasi-Newton optimization algorithm selects the new inverse Hessian approximation
at each step to be the “optimally conditioned” member of a certain one-parameter class of rank two updates to the last inverse Hessian approximationH. In this paper we show that virtually the same goals of conditioning can be achieved while restricting
to the convex class of updates, which are bounded by the popular DFP and BFGS updates. This suggests the computational testing of alternatives to the “optimal conditioning” strategy.
at each step to be the “optimally conditioned” member of a certain one-parameter class of rank two updates to the last inverse Hessian approximationH. In this paper we show that virtually the same goals of conditioning can be achieved while restricting to the convex class of updates, which are bounded by the popular DFP and BFGS updates. This suggests the computational testing of alternatives to the “optimal conditioning” strategy.Accelerating Research
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