Geodesic
Finding the principal points of a random variable
Carrizosa, Emilio ; Conde, E. ; Castaño, A.1 ; Romero-Morales, D.2
1 Departamento de Matemáticas, E.U. Empresariales, Universidad de Cádiz, C/ Por Vera, N. 54, Jerez de la Frontera, Cádiz, Spain.
2 Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 35 (2001) no. 3, pp. 315-328

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The p-principal points of a random variable X with finite second moment are those p points in ℝ minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.

Keywords: principal points, d.c. functions, branch and bound

Carrizosa, Emilio  ; Conde, E.  ; Castaño, A. 1 ; Romero-Morales, D. 2

1 Departamento de Matemáticas, E.U. Empresariales, Universidad de Cádiz, C/ Por Vera, N. 54, Jerez de la Frontera, Cádiz, Spain.
2 Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands. 
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     author = {Carrizosa, Emilio and Conde, E. and Casta\~no, A. and Romero-Morales, D.},
     title = {Finding the principal points of a random variable},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {315--328},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {3},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RO_2001__35_3_315_0/}
}
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Carrizosa, Emilio; Conde, E.; Castaño, A.; Romero-Morales, D. Finding the principal points of a random variable. RAIRO - Operations Research - Recherche Opérationnelle, Tome 35 (2001) no. 3, pp. 315-328. http://geodesic.mathdoc.fr/item/RO_2001__35_3_315_0/