simplex

单纯形
#probability #convex_optimization

Definition

For any finite set $A$ , denote by $\Delta(A)$ the set of all probability distributions over $A$ . That is,

\Delta(A) := \left\{ p : A \to [0,1] : \sum_{a \in A} p(a) = 1 \right\}

The set $\Delta(A)$ is termed a simplex in $\mathbb{R}^{|A|}$ .

Notes

simplex is a polytope
simplex algorithm allows efficiently solving extreme points of a polytope, used in linear programming

References

M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 146.
https://en.wikipedia.org/wiki/Simplex
https://optimization.cbe.cornell.edu/index.php?title=Simplex_algorithm