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Table 1 Three examples of loss of functions

From: Parallel coordinate descent methods for big data optimization

Square loss \(\tfrac{1}{2}(A_j^T x - y_j)^2\)
Logistic loss \(\log (1 + e^{-y_j A_j^T x})\)
Hinge square loss \(\tfrac{1}{2}\max \{0, 1- y_j A_j^Tx\}^2\)