Learn More
A complex frame is a collection of vectors that span C M and define measurements , called intensity measurements, on vectors in C M. In purely mathematical terms, the problem of phase retrieval is to recover a complex vector from its intensity measurements, namely the modulus of its inner product with these frame vectors. We show that any vector is uniquely(More)
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Sums of squares Semidefinite programming Gale duality a b s t r a c t A smooth quartic(More)
We present a complex frame of eleven vectors in 4-space and prove that it defines injective measurements. That is, any rank-one 4 × 4 Hermitian matrix is uniquely determined by its values as a Hermitian form on this collection of eleven vectors. This disproves a recent conjecture of Bandeira, Cahill, Mixon, and Nelson. We use algebraic computations(More)
Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem: an algebraic approach via solving polynomial equations, a(More)
The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over any region in the associated hyperplane arrangement. We determine the degree, arithmetic genus and defining prime(More)
Real Algebraic Geometry in Convex Optimization In the past twenty years, a strong interplay has developed between convex optimization and algebraic geometry. Algebraic geometry provides necessary tools to analyze the behavior of solutions, the geometry of feasible sets, and to develop new relaxations for hard non-convex problems. On the other hand,(More)