1. The negative log-likelihood of the correct class is typically used as a surrogate for the 0-1 loss.
2. According to Taylor Equation, quasi-Newton method use some reversible symmetric matrix to take place of the original Hessian Matrix.
3. Convex extension methods and disjunctive programming methods.

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Surrogate loss function is a proxy having consistency or calibration with the original loss function, which is not comfortable for people to use derivatives or other direct method to optimize.

Surrogate Loss Function

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

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