Geodesic
Adaptive convex optimization in Banach spaces: a multilevel approach
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 263-287

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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. 
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     author = {Canuto, Claudio},
     title = {Adaptive convex optimization in {Banach} spaces: a multilevel approach},
     journal = {Bollettino della Unione matematica italiana},
     pages = {263--287},
     publisher = {mathdoc},
     volume = {Ser. 8, 6B},
     number = {2},
     year = {2003},
     zbl = {1177.42028},
     mrnumber = {MR1988205},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_2_a0/}
}
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Canuto, Claudio. Adaptive convex optimization in Banach spaces: a multilevel approach. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 263-287. http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_2_a0/