Spectrahedral cones generated by rank 1 matrices
نویسندگان
چکیده
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 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 کاملExponential lower bounds on spectrahedral representations of hyperbolicity cones
The Generalized Lax Conjecture asks whether every hyperbolicity cone is a section of a semidefinite cone of sufficiently high dimension. We prove that the space of hyperbolicity cones of hyperbolic polynomials of degree d in n variables contains (n/d) pairwise distant cones in the Hausdorff metric, and therefore that any semidefinite representation of such polynomials must have dimension at lea...
متن کاملPolynomial-sized semidefinite representations of derivative relaxations of spectrahedral cones
We give explicit polynomial-sized (in n and k) semidefinite representations of the hyperbolicity cones associated with the elementary symmetric polynomials of degree k in n variables. These convex cones form a family of non-polyhedral outer approximations of the non-negative orthant that preserve low-dimensional faces while successively discarding high-dimensional faces. More generally we const...
متن کاملA note on the CP-rank of matrices generated by Soules matrices
It is proved that a nonnegative matrix generated by a Soules matrix is a completely positive matrix with cp-rank equal to the rank.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Global Optimization
سال: 2015
ISSN: 0925-5001,1573-2916
DOI: 10.1007/s10898-015-0313-4