Questions about the property of convergence on theorem 5.4 and 5.5 about nash-mtl HOT 1 CLOSED

Hi @BossunWang
Thanks for your interest in our work.

1. This is the 2-norm (Euclidean norm). There's a known result (https://math.stackexchange.com/questions/2330716/proving-that-the-norm-of-a-matrix-is-bigger-or-equal-to-its-smallest-singular-v) that shows the required inequality in the proof.
2. In the paper, we assume that the gradients are linearly independent unless we are at a Pareto
   stationary point. However, note that this generally need not hold; for example, take the degenerate case of two identical tasks.

from nash-mtl.