Geodesic
Curvature-based multistep quasi-Newton method for unconstrained optimization
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 3, pp. 281-293

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Multi-step methods derived in [1–3] have proven to be serious contenders in practice by outperforming traditional quasi-Newton methods based on the linear Secant Equation. Minimum curvature methods that aim at tuning the interpolation process in the construction of the new Hessian approximation of the multi-step type are among the most successful so far [3]. In this work, we develop new methods of this type that derive from a general framework based on a parameterized nonlinear model. One of the main concerns of this paper is to conduct practical investigation and experimentation of the newly developed methods and we use the methods in [1–7] as a benchmark for the comparison. The results of the numerical experiments made indicate that these methods substantially improve the performance of quasi-Newton methods. 
@article{SJVM_1999_2_3_a6,
     author = {I. A. R. Moghrabi and Samir A. Obeid},
     title = {Curvature-based multistep {quasi-Newton} method for unconstrained optimization},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {281--293},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_3_a6/}
}
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I. A. R. Moghrabi; Samir A. Obeid. Curvature-based multistep quasi-Newton method for unconstrained optimization. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 3, pp. 281-293. http://geodesic.mathdoc.fr/item/SJVM_1999_2_3_a6/