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On the minimum volume simplex enclosure problem for estimating a linear mixing model

Author

Listed:
  • E. Hendrix
  • I. García
  • J. Plaza
  • A. Plaza

Abstract

We describe the minimum volume simplex enclosure problem (MVSEP), which is known to be a global optimization problem, and further investigate its multimodality. The problem is a basis for several (unmixing) methods that estimate so-called endmembers and fractional values in a linear mixing model. We describe one of the estimation methods based on MVSEP. We show numerically that using nonlinear optimization local search leads to the estimation results aimed at. This is done using examples, designing instances and comparing the outcomes with a maximum volume enclosing simplex approach which is used frequently in unmixing data. Copyright The Author(s) 2013

Suggested Citation

  • E. Hendrix & I. García & J. Plaza & A. Plaza, 2013. "On the minimum volume simplex enclosure problem for estimating a linear mixing model," Journal of Global Optimization, Springer, vol. 56(3), pages 957-970, July.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:3:p:957-970
    DOI: 10.1007/s10898-012-9876-5
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    References listed on IDEAS

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    1. Peng Sun & Robert M. Freund, 2004. "Computation of Minimum-Volume Covering Ellipsoids," Operations Research, INFORMS, vol. 52(5), pages 690-706, October.
    2. Buti,Marco & Deroose,Servaas & Gaspar,Vitor & Martins,João Nogueira (ed.), 2010. "The Euro," Cambridge Books, Cambridge University Press, number 9789279098420, October.
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