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On the separability of multivariate functions

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  • Goda, Takashi

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.

Suggested Citation

  • Goda, Takashi, 2019. "On the separability of multivariate functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 210-219.
  • Handle: RePEc:eee:matcom:v:159:y:2019:i:c:p:210-219
    DOI: 10.1016/j.matcom.2018.11.015
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    References listed on IDEAS

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    1. Marco Ratto, 2008. "Analysing DSGE Models with Global Sensitivity Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 115-139, March.
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