Large scale unconstrained optimization.

*(English)*Zbl 0881.65055
Duff, I. S. (ed.) et al., The state of the art in numerical analysis. Based on the proceedings of a conference organized by the Institute of Mathematics and its Applications (IMA), University of York, York, GB, April 1–4, 1996. Oxford: Clarendon Press. Inst. Math. Appl. Conf. Ser., New Ser. 63, 311-338 (1997).

Summary: This paper reviews advances in Newton, quasi-Newton and conjugate gradient methods for large scale optimization. It also describes several packages developed during the last ten years, and illustrates their performance on some practical problems. Much attention is given to the concept of partial separability which is gaining importance with the arrival of automatic differentiation tools and of optimization software that fully exploits its properties.

For the entire collection see [Zbl 0869.00046].

For the entire collection see [Zbl 0869.00046].

##### MSC:

65K05 | Numerical mathematical programming methods |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

90C30 | Nonlinear programming |

90C06 | Large-scale problems in mathematical programming |

65Y15 | Packaged methods for numerical algorithms |

##### Keywords:

survey paper; quasi-Newton method; conjugate gradient methods; large scale optimization; packages; performance; partial separability; automatic differentiation
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\textit{J. Nocedal}, in: The state of the art in numerical analysis. Based on the proceedings of a conference organized by the Institute of Mathematics and its Applications (IMA), University of York, York, GB, April 1--4, 1996. Oxford: Clarendon Press. 311--338 (1997; Zbl 0881.65055)