Adaptive convex optimization in Banach spaces: a multilevel approach

Claudio Canuto

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 2, page 263-287
  • ISSN: 0392-4041

Abstract

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This is mainly a review paper, concerned with some applications of the concept of Nonlinear Approximation to adaptive convex minimization. At first, we recall the basic ideas and we compare linear to nonlinear approximation for three relevant families of bases used in practice: Fourier bases, finite element bases, wavelet bases. Next, we show how nonlinear approximation can be used to design rigorously justified and optimally efficient adaptive methods to solve abstract minimization problems in Banach spaces, using either wavelet or finite element bases. In particular, a wavelet adaptive steepest-descent algorithm is presented and investigated.

How to cite

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Canuto, Claudio. "Adaptive convex optimization in Banach spaces: a multilevel approach." Bollettino dell'Unione Matematica Italiana 6-B.2 (2003): 263-287. <http://eudml.org/doc/195377>.

@article{Canuto2003,
abstract = {This is mainly a review paper, concerned with some applications of the concept of Nonlinear Approximation to adaptive convex minimization. At first, we recall the basic ideas and we compare linear to nonlinear approximation for three relevant families of bases used in practice: Fourier bases, finite element bases, wavelet bases. Next, we show how nonlinear approximation can be used to design rigorously justified and optimally efficient adaptive methods to solve abstract minimization problems in Banach spaces, using either wavelet or finite element bases. In particular, a wavelet adaptive steepest-descent algorithm is presented and investigated.},
author = {Canuto, Claudio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {263-287},
publisher = {Unione Matematica Italiana},
title = {Adaptive convex optimization in Banach spaces: a multilevel approach},
url = {http://eudml.org/doc/195377},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Canuto, Claudio
TI - Adaptive convex optimization in Banach spaces: a multilevel approach
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/6//
PB - Unione Matematica Italiana
VL - 6-B
IS - 2
SP - 263
EP - 287
AB - This is mainly a review paper, concerned with some applications of the concept of Nonlinear Approximation to adaptive convex minimization. At first, we recall the basic ideas and we compare linear to nonlinear approximation for three relevant families of bases used in practice: Fourier bases, finite element bases, wavelet bases. Next, we show how nonlinear approximation can be used to design rigorously justified and optimally efficient adaptive methods to solve abstract minimization problems in Banach spaces, using either wavelet or finite element bases. In particular, a wavelet adaptive steepest-descent algorithm is presented and investigated.
LA - eng
UR - http://eudml.org/doc/195377
ER -

References

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