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Local Optimization of Black-Box Function with High or Infinite-Dimensional Inputs

Roche, Angelina (2018), Local Optimization of Black-Box Function with High or Infinite-Dimensional Inputs, Computational Statistics, 33, 1, p. 467–485. 10.1007/s00180-017-0751-1

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Type
Article accepté pour publication ou publié
Date
2018
Journal name
Computational Statistics
Volume
33
Number
1
Publisher
Physica-Verl
Pages
467–485
Publication identifier
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Author(s)
Roche, Angelina
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Mathématiques Appliquées Paris 5 [MAP5 - UMR 8145]
Abstract (EN)
Black-box optimization problems when the input space is a high-dimensional space or a function space appear in more and more applications. In this context, the methods available for finite-dimensional data do not apply. The aim is then to propose a general method for optimization involving dimension reduction techniques. Different dimension reduction basis are considered (including data-driven basis). The methodology is illustrated on simulated functional data. The choice of the different parameters, in particular the dimension of the approximation space, is discussed. The method is finally applied to a problem of nuclear safety.
Subjects / Keywords
Response Surface Methodology; Design of Experiments; Functional data analysis; Black-box optimization