**Problem 5.**

$$\min\_{\mathbf{C}\_{\mathbf{L}}(\mathbf{w}, \mathbf{C}, \mathbf{a}) \in \mathcal{X} \times \mathbb{R} \times \mathbb{R}^{\mathbb{R}^{K}}} \mathbf{C} \tag{21}$$

*<sup>s</sup>*.*t*.*F<sup>L</sup>*(*<sup>w</sup>*, *<sup>α</sup>k*|*βk*) ≤ *C* + *WCβk* (*k* = 1, . . . , *K*) (22)

*where α* = (*<sup>α</sup>*1, ··· , *<sup>α</sup>K*)*.*

> According to the Lemma 2, Problem 3 and 5 are equivalent.
