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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…
Local geometry of feasible regions via smooth paths
Adrian S. Lewis, Adriana Nicolae, Tonghua Tian
Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightfo…
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…
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…