Attempts to create and solve a function called the generalized Lagrangian
1) Describe the set, $\mathbb{S}$, in terms of equations and inequalities
2) Introduce the variables $\lambda$ and $\alpha$ to get the generalized Lagrangian
3) Optimize  $min_{x}$ $max_{\lambda}$ $max_{\alpha,\alpha\ge0}$ $\mathop{\mathcal{L}}(x, \lambda, \alpha)$

This approach can be used as a parameter norm penalty by which to regularize the cost function. 

Karush-Kuhn-Tucker Approach (KKT)

Finding the minimum or maximum value of a function, $f(x)$, over a set of inputs, $\mathbb{S}$.  Points in $\mathbb{S}$ are called feasible points.

Michigan State University

- Computation of transforms
- Computations in finite fields
- Computations on matrices
- Computations on polynomials
- Number-theoretic computations
- Interpolation
- Numerical differentiation
- Interval arithmetic
- Arbitrary-precision arithmetic
- Automatic differentiation
- Mesh generation
- Discretization

Numerical Analysis

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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