Algebras Associated to Bruhat Intervals and Polyhedral Cones

A theorem on the existence of a solution under feasibility assumptions to a convex minimization problem over polyhedral cones in complex space is given by using the fact that the problem of solving a convex minimization program naturally leads to the consideration of the following nonlinear complementarity problem: given g: Cn → Cn, find z such that g(z) ∈ S*, z ∈ S, and Re〈g(z), z〉 = 0, where S is a polyhedral cone and S* its polar.

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An algorithm for the computation of perfect polyhedral cones over real quadratic number fields

EUROCAL '85 - Lecture Notes in Computer Science ◽

10.1007/3-540-15984-3_317 ◽

1985 ◽

pp. 487-488

Author(s):

H. Ong ◽

D. Golke

Keyword(s):

Number Fields ◽

Quadratic Number ◽

Polyhedral Cones ◽

Quadratic Number Fields ◽

Real Quadratic

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On minimal positive basis for polyhedral cones in

Linear and Multilinear Algebra ◽

10.1080/03081087.2021.1973360 ◽

2021 ◽

pp. 1-17

Author(s):

M. B. Alves ◽

J. B. Gomes ◽

K. M. Pedroso

Keyword(s):

Polyhedral Cones ◽

Positive Basis

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Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids

International Mathematics Research Notices ◽

10.1093/imrn/rnaa124 ◽

2020 ◽

Cited By ~ 1

Author(s):

Fabrizio Caselli ◽

Michele D’Adderio ◽

Mario Marietti

Keyword(s):

Coxeter Group ◽

Coxeter Groups ◽

Combinatorial Properties ◽

Coxeter Matroid ◽

Finite Coxeter Group ◽

Bruhat Intervals

Abstract We provide a weaker version of the generalized lifting property that holds in complete generality for all Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also describe some combinatorial properties of the associated polytopes.

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Characterizations of Fully Constrained Poses of Parallel Cable-Driven Robots: A Review

Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2008-49467 ◽

2008 ◽

Cited By ~ 9

Author(s):

Marc Gouttefarde

Keyword(s):

Linear Algebra ◽

Convex Cones ◽

Mobile Platform ◽

Polyhedral Cones ◽

Fundamental Properties ◽

Special Cases ◽

Force Closure

The pose of the mobile platform of a parallel cable-driven robot is said to be fully constrained if any wrench can be created at the platform by pulling on it with the cables. A fully constrained pose is also known as a force-closure pose. In this paper, a review of three useful characterizations of a force-closure pose is proposed. These characterizations are stated in the form of theorems for which proofs are presented. Tools from linear algebra allow to derive some of these proofs while the others are more difficult and can hardly be obtained in this manner. Therefore, polyhedral cones, which are special cases of convex cones, are introduced along with some of their well-known fundamental properties. Then, it is shown how the aforementioned difficult proofs can be obtained as direct consequences of these properties.

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