Searching for critical angles in a convex cone

Authors:
Alfredo Iusem;Alberto Seeger
Affiliations:
Estrada Dona Castorina, Instituto de Matemática Pura e Aplicada, 110-Jardim Botânico, Rio de Janeiro, Brazil;University of Avignon, Department of Mathematics, 33, rue Pasteur, 84000, Avignon, France
Venue:
Mathematical Programming: Series A and B - Series B - Special Issue: Nonsmooth Optimization and Applications
Year:
2009

Citing 0
Cited 4

Antipodal pairs, critical pairs, and Nash angular equilibria in convex cones

Optimization Methods & Software
Local minima of quadratic forms on convex cones

Journal of Global Optimization
A Variational Approach to Copositive Matrices

SIAM Review
Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

The concept of antipodality relative to a closed convex cone has been explored in detail in a recent work of ours. The antipodality problem consists of finding a pair of unit vectors in K achieving the maximal angle of the cone. Our attention now is focused not just in the maximal angle, but in the angular spectrum of the cone. By definition, the angular spectrum of a cone is the set of angles satisfying the stationarity (or criticality) condition associated to the maximization problem involved in the determination of the maximal angle. In the case of a polyhedral cone, the angular spectrum turns out to be a finite set. Among other results, we obtain an upper bound for the cardinality of this set. We also discuss the link between the critical angles of a cone K and the critical angles of its dual cone.