Geodesic
Curvature-based multistep quasi-Newton method for unconstrained optimization
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 3, pp. 281-293 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] Moghrabi I. A. R., Obeid S. Y., “A new family of multi-step quasi-Newton methods”, 6-th Int. Coll. on Differential Equations, ed. Bainov D., VSP, 1998, 319–326 | MR | Zbl

[2] Ford J. A., Moghrabi I. A., “Minimum curvature quasi-Newton methods”, Computers Math. Applic., 31 (1996), 179–186 | DOI | MR | Zbl

[3] Ford J. A., Moghrabi L. A., Function-value multi-step quasi-Newton methods, Technical Report; CSM-270, Department of Computer Science, University of Essex, 1996

[4] Ford J. A., Moghrabi L. A., On the use function value in multi-step methods, Technical Report; CSM-271, Department of Computer Science, University of Essex, 1996 | Zbl

[5] Ford J. A., Moghrabi L. A., “Further investigation of multi-step quasi-Newton methods”, Scientia Iranica, 1 (1995), 327–334 | MR | Zbl

[6] Ford J. A., Moghrabi L. A., “Multi-step quasi-Newton methods for optimization”, J. Comput. Appl. Math., 50 (1994), 305–323 | DOI | MR | Zbl

[7] Ford J. A., Moghrabi L. A., “Alternative parameter choices for multi-step quasi-Newton methods”, Optim. Meth. Software, 2 (1993), 357–370 | DOI

[8] Gill P., Murray W., Wright M., Numerical Linear Algebra on Optimization, v. I, Addison-Wesley, U.S.A, 1991

[9] Fletcher R. F., Pratical Methods of Optimization, John Wiley, Great Britain, 1991 | MR

[10] Ford J. A., Saadallah A. F., “Efficient utilization of function-values in unconstrained minimization”, Colloq. Math. Soc. Jan. Bolyai, 50 (1986), 539–563

[11] Dennis J. E., Schnabel R. B., “Minimum change variable metric update formulae”, SIAM Review, 21 (1979), 443–459 | DOI | MR | Zbl

[12] Broyden C. G., “The convergence of a class of double-rank minimization algorithms”, J. Inst. Math. Applic., 6 (1970), 76–90 ; 222–231 | DOI | MR | Zbl | Zbl

[13] Fletcher R., “A new approach to variable metric algorithms”, Comput. J., 13 (1970), 317–322 | DOI | Zbl

[14] Goldfarb D., “A family of variable metric methods derived by variational means”, Maths. Comp., 24 (1970), 23–26 | MR

[15] Shanno D. F., “Conditioning of quasi-Newton methods for function minimization”, Maths. Comp., 24 (1970), 647–656 | MR