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2014

Action constrained quasi-Newton methods

Gower, Robert Mansel, Gondzio, Jacek

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At the heart of Newton based optimization methods is a sequence of symmetric linear systems.

Each consecutive system in this sequence is similar to the next, so solving them separately is a waste of computational effort.
Here we describe automatic preconditioning techniques for iterative methods for solving such sequences of systems by maintaining an estimate of the inverse system matrix.
We update the estimate of the inverse system matrix with quasi-Newton type formulas based on what we call an action constraint instead of the secant equation.

Action constrained quasi-Newton methods · Around

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Jurjen Duintjer Tebbens
1941
Earlier work this paper cites.
Max A Woodbury
1950
Earlier work this paper cites.
M. R. Hestenes and E. Stiefel
1952
Earlier work this paper cites.
W. C Davidon
1959
Earlier work this paper cites.
By R Fletcher and M J D Powell
1963
Earlier work this paper cites.
CG Broyden
1965
Earlier work this paper cites.
By J Greenstadt
1969
Earlier work this paper cites.
C. G. Broyden
1970
Earlier work this paper cites.
Rodger Fletcher
1970
Earlier work this paper cites.
Donald Goldfarb
1970
Earlier work this paper cites.
D F Shanno
1971
Earlier work this paper cites.
J. E. Jr. Dennis and R. B. Schnabel
1979
Earlier work this paper cites.
JJ Moré and DC Sorensen
1979
Earlier work this paper cites.
Jorge Nocedal
1980
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