A course in convexity

By Alexander I. Barvinok. Graduate Studies in Mathematics, 2002

910 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/245792725673c8c375df773a16847c38b40d542f

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Citations in the corpus

Distance geometry and data science (2019, methodology): “ (39) (see Barvinok 1995 and Barvinok 2002, §6.2), but these do not allow the user to specify an arbitrary rank K, so they only apply to the EDMCP.”
Notes About the Carathéodory Number (2011, background): “It is also known [5, 15] that a convex curve in R (that is, a curve with no n + 1 points in a single affine hyperplane) has Carathéodory number at most n+2 2 .”
The Reflexive Dimension of a Lattice Polytope (2004, methodology): “So in particular, refldim([0, 11]) = 4 > 3 = refldim([0, 12]), and the reflexive dimension of line segments is not monotone in `, as could also be seen from refldim([0, 1]) = 2 > 1 = refldim([0, 2]).”
About the Connes embedding conjecture (2013, neutral): “Theorem 3 (Eidelheit–Kakutani ([Ba])).”
Breaking the Curse of Dimensionality with Convex Neural Networks (2014, methodology): “Given standard results (see, e.g. Barvinok, 2002), a (1/ √ d)-scaled version of the ellipsoid is inscribed in this polytope, and thus the ellipsoid is a provably good approximation of the zonotope with a factor scaling as √ d.”
Robust Energy Management of Microgrid With Uncertain Renewable Generation and Load (2016, methodology): “For the linear model, according to convex theory [35] and extreme scenario theory [15], extreme solutions exist in the bounds or endpoints.”
Piecewise polynomials, Minkowski weights, and localization on toric varieties (2007, background): “dron containing a line to 0 [ Bar02 , Theorem VIII.3.3].”
Geometric Approximation Algorithms (2011, methodology): “We closely follow the exposition of Barvinok [Bar02].”
Theory of semidefinite programming for Sensor Network Localization (2005, neutral): “Indeed, most of the previous works on the Sensor Network Localization problem fall into two categories – one deals with computing a realization of a given instance [12,14, 15,21,26–28, 30 ], and the other deals with determining whether a given”
Cone-volume measures of polytopes (2013, background): “Good general references on these topics are the books by Barvinok [3], Gardner [7], Gruber [10], Schneider [25] and Ziegler [28].”
Cones and interior-point algorithms for structured convex optimization involving powers andexponentials (2009, methodology): “In Chapter 3 we formulated three conjectures for self-concordant barriers: an (n + 1)-self-concordant barrier for the high-dimensional power cone K α and for a further a generalization of K α , and (partial) scaling of the 3-self-concordant barrier for Kα which results in a self-concordance paramete”