8 papers · 1 filter
Strong growth and Goldstein subgradients in piecewise smooth optimization
Adrian S. Lewis, Fahaar M. Pirani
We explore a new growth condition for Lipschitz functions around local minimizers, recently proposed in the context of Goldstein-subgradient-based algorithms and their behavior in…
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…
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…
Lipschitz minimization and the Goldstein modulus
Siyu Kong, Adrian S. Lewis
Goldstein's 1977 idealized iteration for minimizing a Lipschitz objective fixes a distance - the step size - and relies on a certain approximate subgradient. That "Goldstein subgra…