A new family of multi-step quasi-Newton algorithms for unconstrained optimization
This work aims at ensuring smoothness of interpolation in both the iterate and the gradient spaces in the so-called multi-step quasi-Newton methods. It concentrates on deriving a variable-metric family of minimum curvature algorithms for unconstrained optimization. The derivation is based on conside...
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| Format: | article |
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1999
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| Online Access: | http://hdl.handle.net/10725/2698 https://www.researchgate.net/publication/268018303_A_new_family_of_multi-step_quasi-Newton_algorithms_for_unconstrained_optimization |
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| Summary: | This work aims at ensuring smoothness of interpolation in both the iterate and the gradient spaces in the so-called multi-step quasi-Newton methods. It concentrates on deriving a variable-metric family of minimum curvature algorithms for unconstrained optimization. The derivation is based on considering a rational model, with a certain tuning parameter, where the aim is to develop a general framework that encompasses all possible two-step minimum curvature algorithms generated by appropriate parameter choices. One member of the family is tested against earlier developed algorithms of the multi-step type. Performance improvement is evident in our presented results, thus verifying the importance of the minimum curvature framework |
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