منابع مشابه
Kernel Polytope Faces Pursuit
Polytope Faces Pursuit (PFP) is a greedy algorithm that approximates the sparse solutions recovered by 1 regularised least-squares (Lasso) [4,10] in a similar vein to (Orthogonal) Matching Pursuit (OMP) [16]. The algorithm is based on the geometry of the polar polytope where at each step a basis function is chosen by finding the maximal vertex using a path-following method. The algorithmic comp...
متن کاملThe stable admissions polytope
The stable admissions polytope – the convex hull of the stable assignments of the university admissions problem – is described by a set of linear inequalities. It depends on a new characterization of stability and arguments that exploit and extend a graphical approach that has been fruitful in the analysis of the stable marriage problem.
متن کاملThe Number of Faces of a Simplicial Convex Polytope
Let P be a simplicial convex d-polytope with fi = fi(P) faces of dimension i. of integers was necessary and sufficient for f to be the f-vector of some simplicial convex d-polytope. Billera and Lee [l] proved the sufficiency of McMullen's condition. In this paper we prove necessity. Thus McMullen's conjecture is completely verified. First we describe McMullen's condition. Given a simplicial con...
متن کاملThe Number of k -Faces of a Simple d -Polytope
Consider the question: Given integers k < d < n, does there exist a simple d-polytope with n faces of dimension k? We show that there exist numbers G(d; k) and N (d; k) such that for n > N (d; k) the answer is yes if and only if G(d; k) divides n. Furthermore, a formula for G(d; k) is given, showing that e.g. G(d; k) = 1 if k d+1 2 or if both d and k are even, and also in some other cases (mean...
متن کاملCritical Facets of the Stable Set Polytope
A facet of the stable set polytope of a graph G can be viewed as a generalization of the notion of an-critical graph. We extend several results from the theory of-critical graphs to facets. The defect of a nontrivial, full-dimensional facet P v2V a(v)x v b of the stable set polytope of a graph G is deened by = P v2V a(v) ?2b. We prove the upper bound a(u) + for the degree of any vertex u in a c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1976
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1976-14037-2