On minimal positive basis for polyhedral cones in

2021 ◽  
pp. 1-17
Author(s):  
M. B. Alves ◽  
J. B. Gomes ◽  
K. M. Pedroso
Keyword(s):  
Polyhedral Cones ◽  
Positive Basis

On an application of the complex nonlinear complementarity problem

1976 ◽  
Vol 15 (1) ◽  
pp. 141-148 ◽  
Author(s):  
J. Parida ◽  
B. Sahoo
Keyword(s):  
Minimization Problem ◽  
Complementarity Problem ◽  
Complex Space ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Polyhedral Cones ◽  
Existence Of A Solution ◽  
Nonlinear Complementarity

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.

scholarly journals Lower and Upper Bounds for Positive Bases of Skein Algebras

2020 ◽  
Author(s):  
Thang T Q Lê ◽  
Dylan P Thurston ◽  
Tao Yu
Keyword(s):  
Chebyshev Polynomials ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Positive Basis ◽  
Positive Bases ◽  
Skein Algebras

Abstract We show that if a sequence of normalized polynomials gives rise to a positive basis of the skein algebra of a surface, then it is sandwiched between the two types of Chebyshev polynomials. For the closed torus, we show that the normalized sequence of Chebyshev polynomials of type one $(\hat{T}_n)$ is the only one that gives a positive basis.

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

2008 ◽  
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.

scholarly journals Maximal exponents of polyhedral cones (III)

2013 ◽  
Vol 365 (7) ◽  
pp. 3535-3573
Author(s):  
Raphael Loewy ◽  
Micha A. Perles ◽  
Bit-Shun Tam
Keyword(s):  
Polyhedral Cones
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