scholarly journals Saturation points on faces of a rational polyhedral cone

2008 ◽  
pp. 147-161 ◽  
Author(s):  
Akimichi Takemura ◽  
Ruriko Yoshida
Keyword(s):  
Polyhedral Cone

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 A New Jacobian-Like Method for the Polyhedral Cone-Constrained Eigenvalue Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Guo Sun
Keyword(s):  
Global Convergence ◽  
Eigenvalue Problem ◽  
Numerical Experiments ◽  
Quadratic Convergence ◽  
Polyhedral Cone ◽  
System Of Equations ◽  
Local Quadratic Convergence ◽  
Ncp Function

The eigenvalue problem over a polyhedral cone is studied in this paper. Based on the F-B NCP function, we reformulate this problem as a system of equations and propose a Jacobian-like method. The global convergence and local quadratic convergence of the proposed method are established under suitable assumptions. Preliminary numerical experiments for a special polyhedral cone are reported in this paper to show the validity of the proposed method.

CONES OF CURVES AND OF LINE BUNDLES ON SURFACES ASSOCIATED WITH CURVES HAVING ONE PLACE AT INFINITY

2002 ◽  
Vol 84 (3) ◽  
pp. 559-580 ◽  
Author(s):  
ANTONIO CAMPILLO ◽  
OLIVIER PILTANT ◽  
ANA J. REGUERA-LÓPEZ
Keyword(s):  
Polyhedral Cone ◽  
Subject Classification ◽  
Factorization Theorem ◽  
Line Bundles ◽  
Unique Factorization ◽  
Primary 14C20 ◽  
New Class ◽  
Secondary 14E05 ◽  
Cone Of Curves ◽  
Projective Surfaces

Let V be a pencil of curves in ${\bf P}^2$ with one place at infinity, and $X \longrightarrow {\bf P}^2$ the minimal composition of point blow-ups eliminating its base locus. We study the cone of curves and the cones of numerically effective and globally generated line bundles on X. It is proved that all of these cones are regular. In particular, this result provides a new class of rational projective surfaces with a rational polyhedral cone of curves. The surfaces in this class have non-numerically effective anticanonical sheaf if the pencil is neither rational nor elliptic. An application is a global version on X of Zariski's unique factorization theorem for complete ideals. We also define invariants of the semigroup of globally generated line bundles on X depending only on the topology of V at infinity.2000 Mathematical Subject Classification: primary 14C20; secondary 14E05.

scholarly journals An extreme positive operator on a polyhedral cone

1988 ◽  
Vol 30 (3) ◽  
pp. 347-348
Author(s):  
A. Guyan Robertson
Keyword(s):  
Positive Operator ◽  
Positive Operators ◽  
Polyhedral Cone ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Extreme Rays

In [2], R. Loewy and H. Schneider studied positive linear operators on circular cones. They characterised the extremal positive operators on these cones and noticed that such operators preserve the set of extreme rays of the cone in this case. They then conjectured that this property of extremal positive operators is true in general.

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