77 citations · 318 across the 57 of their papers we have counts for
5 papers · 1 filter
Curves of Descent
D. Drusvyatskiy, A. D. Ioffe, A. S. Lewis
Steepest descent is central in variational mathematics. We present a new transparent existence proof for curves of near-maximal slope --- an influential notion of steepest descent…
Clarke subgradients for directionally Lipschitzian stratifiable functions
Dmitriy Drusvyatskiy, Alexander D. Ioffe, Adrian S. Lewis
Using a geometric argument, we show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally stratifiable) directionally Lips…
Optimality, identifiability, and sensitivity
Dmitriy Drusvyatskiy, Adrian S. Lewis
Around a solution of an optimization problem, an "identifiable" subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A que…
Approximating functions on stratified sets
D. Drusvyatskiy, M. Larsson
We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our resul…
Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential
Dmitriy Drusvyatskiy, Adrian S. Lewis
We prove that uniform second order growth, tilt stability, and strong metric regularity of the limiting subdifferential --- three notions that have appeared in entirely different s…