A refined Newton’s mesh independence principle for a class of optimal shape design problems

• Autorzy: Ioannis Argyros
• Języki publikacji: EN

Abstrakty

EN

Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.

Słowa kluczowe

EN

Mesh independence principle; Newton’s method; radius of convergence; optimal space design; 65K10; 49K20; 49M15; 49M05; 47H17

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 4
• Strony: 562-572

Daty

wydano

2006-12-01

online

2006-12-01

Twórcy

autor

Ioannis Argyros

• Cameron University

Bibliografia

• [1] E.L. Allgower, K. Böhmer, F.A. Potra and W.C. Rheinboldt: “A mesh-independence principle for operator equations and their discretizations”, SIAM J. Numer. Anal., Vol. 23, (1986).
• [2] I.K. Argyros: “A mesh independence principle for equations and their discretizations using Lipschitz and center Lipschitz conditions, Pan”, Amer. Math. J., Vol. 14(1), (2004), pp. 69–82.
• [3] I.K. Argyros: “A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space”, J. Math. Anal. Appl., Vol. 298(2), (2004), pp. 374–397. http://dx.doi.org/10.1016/j.jmaa.2004.04.008
• [4] I.K. Argyros: Newton Methods, Nova Science Publ. Corp., New York, 2005.
• [5] L.V. Kantorovich and G.P. Akilov: Functional Analysis in Normed Spaces, Pergamon Press, Oxford, 1982.
• [6] M. Laumen: “Newton’s mesh independence principle for a class of optimal design problems”, SIAM J. Control Optim., Vol. 37(4), (1999), pp. 1070–1088. http://dx.doi.org/10.1137/S0363012996303529
• [7] W.C. Rheinboldt: “An adaptive continuation process for solving systems of nonlinear equations”, In: Mathematical models and Numerical Methods, Banach Center Publ., Vol. 3, PWN, Warsaw, 1978, 129–142.

Identyfikatory

DOI

10.2478/s11533-006-0027-4