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Minimal enclosing balls via geodesics
Ariel Goodwin, Adrian S. Lewis
Algorithms for minimal enclosing ball problems are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus here on a particularly simpl…
Stochastic and incremental subgradient methods for convex optimization on Hadamard spaces
Ariel Goodwin, Adrian S. Lewis, Genaro López-Acedo +1
As a foundation for optimization, convexity is useful beyond the classical settings of Euclidean and Hilbert space. The broader arena of nonpositively curved metric spaces, which i…
Recognizing weighted means in geodesic spaces
Ariel Goodwin, Adrian S. Lewis, Genaro Lopez-Acedo +1
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we…
Convex optimization on CAT(0) cubical complexes
Ariel Goodwin, Adrian S. Lewis, Genaro Lopez-Acedo +1
We consider geodesically convex optimization problems involving distances to a finite set of points in a CAT(0) cubical complex. Examples include the minimum enclosing ball pro…