I am trying to figure out how to solve:

min_{U }r_{p}

wherer_{p}=α^{⊺}ωandUis a sphere centered atαwith radius equal toχ|α| . (ωis a vector or weights andχlies between 0 and 1.)

i.e. we are trying to minimizerinside the sphere centered at_{p}α.

The authors end up with the following solution:

min_{U }r_{p }=α^{⊺}ω−χ|α| |ω|

The authors hint at Bayesian estimation but I am not familiar with it. Any ideas as to how they may have arrived at this would be great. Many thanks in advance.