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math.OC2024
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…
math.OC2024
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…
math.OC2024
Horoballs and the subgradient method
Adrian S. Lewis, Genaro Lopez-Acedo, Adriana Nicolae
To explore convex optimization on Hadamard spaces, we consider an iteration in the style of a subgradient algorithm. Traditionally, such methods assume that the underlying spaces a…