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A globally convergent modified version of the method of moving asymptotes. (English) Zbl 1499.49089

Summary: A new modified moving asymptotes method is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and explicitly solved. In doing so we propose a strategy to incorporate a modified second-order information for the moving asymptotes location. Under natural assumptions, we prove the geometrical convergence. In addition the experimental results reveal that the present method is significantly faster compared to the [M. Bachar et al., ETNA, Electron. Trans. Numer. Anal. 43, 21–44 (2014; Zbl 1302.65148)] method, Newton’s method and the BFGS Method.

MSC:

49M29 Numerical methods involving duality
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming

Citations:

Zbl 1302.65148
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References:

[1] B. Mostafa, E. Thierry, A. Guessab:A moving asymptotes algorithm using new local convex approximation methods with explicit solutions. Electron. Trans. Numer. Anal., 43 (2014), 21-44. · Zbl 1302.65148
[2] R. L. Burden, J. D. Faires: Numerical Analysis. Cengange Learning, Boston, 2011.
[3] A. Greenbaum and T. P. Chartier: Numerical Methods. Princeton University Press, Princeton, 2012. · Zbl 1247.65001
[4] Allal Guessab, (Received 04.12.2018)
[5] E2S UPPA, CNRS, LMAP, 64000, Pau France E-mail: allal.guessab@univ-pau.fr
[6] Abderrazak Driouch Université de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP, 64000, Pau France E-mail: driouchabderrazak@gmail.com Otheman Nouisser Ibn Tofail Kenitra Morocco E-mail: otheman.nouisser@yahoo.fr
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