Majorization, polyhedra, and statistical testing problems
نویسندگان
چکیده
منابع مشابه
Majorization, Polyhedra and Statistical Testing Problems. Majorization, Polyhedra and Statistical Testing Problems
There are important connections between majorization and convex polyhedra. Both weak majorization and majorization are preorders related to certain simple convex cones. We investigate the facial structure of a polyhedral cone C associated with a layered directed graph. A generalization of weak majorization based on C is introduced. It de nes a preorder of matrices. An application in statistical...
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For integers k and n with k ≤ n a vector x ∈ R is said to be weakly k-majorized by a vector q ∈ R if the sum of the r largest components of x does not exceed the sum of the r largest components of q, for r = 1, . . . , k. For a given q the set of vectors weakly k-majorized by q defines a polyhedron P (q; k). We determine the vertices of both P (q; k) and its integer hull Q(q; k). Furthermore a ...
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We introduce the concept of weak k-majorization extending the classical notion of weak sub-majorization. For integers k and n with k n a vector x 2 R is weakly k-majorized by a vector q 2 R if the sum of the r largest components of x does not exceed the sum of the r largest components of q, for r = 1; : : : ; k. For a given q the set of vectors weakly k-majorized by q de nes a polyhedron P (q;k...
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A vector x E Rn is weakly k-majorized by a vector q 6 R^ if the sum of r largest components of x is less than or equal to the sum of r largest components of q for r = 1,2,. . . , k and k < n. In this paper we extend the components of x to their absolute values in the above description and generalize some results in [2] and [3] by G. Dahl and F. Margot.
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A compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. Directed Hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. Sets of extrema of Birkhoff polyhedra are mapped to tours ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1998
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)00336-4