5.3 Let x1, . . . , xn be distinct points in Rp. Consider the minimization of

with respect to y 2 Rp, where 1, . . . , n are chosen positive weights. The solution of (5.31) is called the L1-multivariate median. If C(y) is strictly convex in Rp and x1, . . . , xn are not collinear, then the minimum is uniquely determined. If x1, . . . , xn lie in a straight line, the minimum is achieved at any one-dimensional median and may not be unique (Vardi and Zhang (2000)).

Transcribed Image Text:

12 C(y)=illy-x|| i=1