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Recursive form of general limited memory variable metric methods. (English) Zbl 1266.49060
Summary: In this report we propose a new recursive matrix formulation of limited memory variable metric methods. This approach can be used for an arbitrary update from the Broyden class (and some other updates) and also for the approximation of both the Hessian matrix and its inverse. The new recursive formulation requires approximately \(4mn\) multiplications and additions per iteration, so it is comparable with other efficient limited memory variable metric methods. Numerical experiments concerning Algorithm 1, proposed in this report, confirm its practical efficiency.

MSC:
49M30 Other numerical methods in calculus of variations (MSC2010)
49K35 Optimality conditions for minimax problems
90C06 Large-scale problems in mathematical programming
90C47 Minimax problems in mathematical programming
90C51 Interior-point methods
Software:
CUTE; CUTEr; L-BFGS
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References:
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