The purpose of this survey is to serve both as a gentle introduction and a coherent overview
of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for …

The paradigm of coresets has recently emerged as a powerful tool for efficiently
approximating various extent measures of a point set P. Using this paradigm, one quickly …

The problem of maximizing a concave function f (x) in the unit simplex Δ can be solved
approximately by a simple greedy algorithm. For given k, the algorithm can find a point x (k) …

We present a general technique for approximating various descriptors of the extent of a set P
of n points in R d when the dimension d is an arbitrary fixed constant. For a given extent …

Geometric data summarization has become an essential tool in both geometric
approximation algorithms and where geometry intersects with big data problems. In linear or …

We present a new data structure for the c-approximate near neighbor problem (ANN) in the
Euclidean space. For n points in ℝ d, our algorithm achieves Oc (n ρ+ d log n) query time …

In optimization or machine learning problems we are given a set of items, usually points in
some metric space, and the goal is to minimize or maximize an objective function over some …

The book provides an overview of the most advanced quantum informational geometric
techniques, which can help quantum communication theorists analyze quantum channels …

We study the problem of computing a (1+ ε)-approximation to the minimum-volume
enclosing ellipsoid of a given point set\cal S={p^ 1, p^ 2,\dots, p^ n\} ⊆\mathbb R^ d. Based …

Given A≔{a1,…, am}⊂ Rd whose affine hull is Rd, we study the problems of computing an
approximate rounding of the convex hull of A and an approximation to the minimum-volume …