Online Lipschitz Selection, Lecture 4/5

Lectures on Online Lipschitz Selection by Sebastien Bubeck for the XIV Escuela de Verano en Matematicas Discretas eventos.cmm.uchile.cl/discreta...
Lecture 4:
- Entropic regularization for MTS on weighted stars
- Multiscale entropic regularization for MTS on trees

[@oriont8242]

in the formula dx_i/dt = -(c_i + mu - kesi_i), why is it that if mu is negative, then the total mass decreases? How do we know c_i - kesi is nonnegative? From complementary slackness kesi_i is only positive when x_i decreases to zero to prevent it from decreasing, but how to see that in this case kesi_i will never be larger than c_i?

[@oriont8242]

sorry i meant why is mu *positive* (since my sign of mu is flipped)