 On the separability of multivariate functionsTakashi Goda Mathematics and Computers in Simulation (MATCOM), 2019, vol. 159, issue C, 210-219 Abstract: Separability of multivariate functions alleviates the difficulty in finding a minimum or maximum value of a function such that an optimal solution can be searched by solving several disjoint problems with lower dimensionalities. In most of practical problems, however, a function to be optimized is black-box and we hardly grasp its separability. In this study, we first describe a general separability condition which a function defined over an arbitrary domain satisfies if and only if the function is separable with respect to given disjoint subsets of variables. By introducing an alternative separability condition, we propose a Monte Carlo-based algorithm to estimate the separability of a function defined over unit cube with respect to given disjoint subsets of variables. Moreover, we extend our algorithm to estimate the number of disjoint subsets and the disjoint subsets such that a function is separable with respect to them. Computational complexity of our extended algorithm is function-dependent and varies from linear to exponential in the dimension. Keywords: Separability; ANOVA decomposition; Multivariate function; Monte Carlo methods (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:159:y:2019:i:c:p:210-219 DOI: 10.1016/j.matcom.2018.11.015 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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