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

Ioannis Argyros

Open Mathematics (2006)

  • Volume: 4, Issue: 4, page 562-572
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Ioannis Argyros. "A refined Newton’s mesh independence principle for a class of optimal shape design problems." Open Mathematics 4.4 (2006): 562-572. <http://eudml.org/doc/269333>.

@article{IoannisArgyros2006,
abstract = {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.},
author = {Ioannis Argyros},
journal = {Open Mathematics},
keywords = {65K10; 49K20; 49M15; 49M05; 47H17},
language = {eng},
number = {4},
pages = {562-572},
title = {A refined Newton’s mesh independence principle for a class of optimal shape design problems},
url = {http://eudml.org/doc/269333},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Ioannis Argyros
TI - A refined Newton’s mesh independence principle for a class of optimal shape design problems
JO - Open Mathematics
PY - 2006
VL - 4
IS - 4
SP - 562
EP - 572
AB - 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.
LA - eng
KW - 65K10; 49K20; 49M15; 49M05; 47H17
UR - http://eudml.org/doc/269333
ER -

References

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  1. [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). Zbl0591.65043
  2. [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. Zbl1057.65027
  3. [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 Zbl1057.65029
  4. [4] I.K. Argyros: Newton Methods, Nova Science Publ. Corp., New York, 2005. 
  5. [5] L.V. Kantorovich and G.P. Akilov: Functional Analysis in Normed Spaces, Pergamon Press, Oxford, 1982. 
  6. [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 Zbl0931.65068
  7. [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. 

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