Online Lipschitz Selection, Lecture 4/5

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Lecture 4:
- Entropic regularization for MTS on weighted stars
- Multiscale entropic regularization for MTS on trees
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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?

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