Vertex Algorithm
The Vertex Algorithm, also known as the Vertex Enumeration Algorithm, is a computational method used to find all the vertices of a convex polytope. A convex polytope is a geometric figure that is defined as the intersection of a finite number of half-spaces. Vertices are the corner points of the polytope, and they play a vital role in solving various optimization and decision-making problems, such as linear programming, game theory, and other areas of operations research. The Vertex Algorithm works by systematically enumerating all vertices of the convex polytope, which can then be utilized to find the optimal solution for the problem at hand.
There are several variations of the Vertex Algorithm, with the most well-known being the Double Description Method and the Fourier-Motzkin Elimination Method. The Double Description Method works by iteratively adding constraints to the polytope and updating the vertices accordingly, while the Fourier-Motzkin Elimination Method uses linear algebra to eliminate variables, thereby reducing the dimensionality of the problem. Both methods have their own advantages and disadvantages in terms of computational complexity, numerical stability, and applicability to different types of polytopes. In practice, the choice of the Vertex Algorithm depends on the specific problem and the desired level of accuracy and computational efficiency.
data class Vertex<T:Comparable<T>>(val data: T) {
override fun toString(): String {
return "$data"
}
}
