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Linear programming is the study of optimizing a linear function over a set of linear inequalities. The Simplex Method, Ellipsoid Method and Interior Point Method are popular algorithms to solve linear programs.

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Testing if a point is inside a convex polytope formed by halfspaces in n-dimension

Assume we have a convex polytope that is formed by the intersection of $k$-halfspaces in $\mathbb{R}^{n}$. $$ a_{0,0}x^{n-1} + {a}_{0,1}x^{n-2} + ... a_{0,n-1} \leq 0 $$ $$ a_{1,0}x^{n-1} + {a}_{1, …
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