5 papers · 1 filter
Nonsmooth Riemannian optimization with inexact manifold primitives via bundle methods
Mateo DÃaz, Benjamin Grimmer, Ian McPherson
Optimization on Hadamard manifolds -- the natural Riemannian setting for globally geodesically convex problems -- relies on exponential maps to retract tangent vectors and parallel…
PDLP: A Practical First-Order Method for Large-Scale Linear Programming
David Applegate, Mateo DÃaz, Oliver Hinder +4
We present PDLP, a practical first-order method for linear programming (LP) designed to solve large-scale LP problems. PDLP is based on the primal-dual hybrid gradient (PDHG) metho…
Active set identification and rapid convergence for degenerate primal-dual problems
Mateo DÃaz, Pedro Izquierdo Lehmann, Haihao Lu +1
Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at…
Preconditioned subgradient method for composite optimization: overparameterization and fast convergence
Mateo DÃaz, Liwei Jiang, Abdel Ghani Labassi
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing appl…
Invariant Kernels: Rank Stabilization and Generalization Across Dimensions
Mateo DÃaz, Dmitriy Drusvyatskiy, Jack Kendrick +1
Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary appli…