منابع مشابه
Smooth hyperbolicity cones are spectrahedral shadows
Hyperbolicity cones are convex algebraic cones arising from hyperbolic polynomials. A well-understood subclass of hyperbolicity cones is that of spectrahedral cones and it is conjectured that every hyperbolicity cone is spectrahedral. In this paper we prove a weaker version of this conjecture by showing that every smooth hyperbolicity cone is the linear projection of a spectrahedral cone, that ...
متن کاملUnbounded Convex Semialgebraic Sets as Spectrahedral Shadows
Recently, Helton and Nie [3] showed that a compact convex semialgebraic set S is a spectrahedral shadow if the boundary of S is nonsingular and has positive curvature. In this paper, we generalize their result to unbounded sets, and also study the effect of the perspective transform on singularities.
متن کاملLecture 8: Spectrahedral Lifts and Positive Semi-definite Rank 1.1 Spectrahedral Lifts
The feasible regions of LPs are polyhedra. Up to linear isomorphism, every polyhedron P can be represented as P + ∩ V where + is the positive orthant and V ⊆ n is an affine subspace. In this context, it makes sense to study other cones that can be optimized over efficiently. A prominent example is the positive semi-definite cone. Let us define Sn sym ⊆ n 2 to be the set of real, symmetric n...
متن کاملShadows.
We investigate the brightness distribution in and around outdoor shadows (for a variety of sky conditions) using modeling and field measurements. The dominant factor influencing the brightness of a shadow is the solid angle subtended by the object blocking the Sun. Occulters at the zenith that subtend a small solid angle cast shadows that are bright and possess a nearly uniform brightness acros...
متن کاملShadows.
It is almost 160 years since Dr James McDonnell delivered an address to the students entering the Belfast General Hospital. Since that time it has fallen upon a member of this staff to welcome those students who have commenced their first year in the clinical branches of medicine. This year it is my privilege and honour to address and welcome you on behalf of the medical and dental staff of thi...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2015
ISSN: 1052-6234,1095-7189
DOI: 10.1137/140978478