99 citations · 157 across the 39 of their papers we have counts for
5 papers · 1 filter
Non-Archimedean Polydisc Spaces and Applications to Optimisation
Paul Lezeau, Yiannis Fam, Anthea Monod +1
We propose a new framework for optimisation over non-Archimedean spaces inspired by Berkovich geometry. Specifically, we introduce polydisc spaces, which consists of products of cl…
Trajectory-Restricted Optimization Conditions and Geometry-Aware Linear Convergence
Faris Chaudhry, Anthea Monod, Keisuke Yano
Linear convergence of first-order methods is typically characterized by global optimization conditions whose constants reflect worst-case geometry of the ambient space. In high-dim…
Tropical Fréchet Means: a polyhedral approach to exact optimization
Kamillo Ferry, Bo Lin, Carlos Améndola +2
The Fréchet mean is a fundamental notion of central tendency defined as a minimizer of a sum of squared distances in a general metric space. In this paper, we study Fréchet means i…
Tropical Gradient Descent
Roan Talbut, Anthea Monod
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interes…
Tropical Optimal Transport and Wasserstein Distances
Wonjun Lee, Wuchen Li, Bo Lin +1
We study the problem of optimal transport in tropical geometry and define the Wasserstein- distances in the continuous metric measure space setting of the tropical projective to…