A counterexample to a ‘simplex algorithm’ for convex bodies
Tóm tắt
A counterexample, in E
3, is given to the following conjecture. Suppose f
* is a linear functional, and e an exposed point of a convex body K such that f
* does not attain its maximum on K at e; then there is an f
*-strictly increasing path in the one-skeleton of K emanating from e. The counterexample shows that a certain generalized ‘simplex algorithm’ fails. Furthermore for a different linear functional f, there are no three disjoint f-strictly increasing paths in the one-skeleton of K leading to e.
Tài liệu tham khảo
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