Functional Representations in Terms of the Extreme Points of Polytopes.
TEXAS UNIV AUSTIN CENTER FOR CYBERNETIC STUDIES
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There exist functions which assign convex combinations of the extreme points of a convex polytope to represent the points of the polytope. Such functions can be taken to be piecewise linear and continuous over the polytope. This result is a consequence of a finite simplicial decomposition of the polytope. When the polytope is rectangular, the function can be taken to be polynomial. An application of such results to linear differential games is also discussed. Author
- Operations Research