Hey gbaileyzn.
Maybe the author is referring to Monte-Carlo techniques (which can be used to compute things like optimization problems as well as integrals): Are you aware of these techniques?
I am trying to figure out how to solve:
min_{U }r_{p}
where r_{p}=α^{⊺}ω and U is a sphere centered at α with radius equal to χ|α| . ( ω is a vector or weights and χ lies between 0 and 1.)
i.e. we are trying to minimize r_{p} inside the sphere centered at 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.