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math.OC2024
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…
math.OC2021★ 3 cited
The structure of conservative gradient fields
Adrian Lewis, Tonghua Tian
The classical Clarke subdifferential alone is inadequate for understanding automatic differentiation in nonsmooth contexts. Instead, we can sometimes rely on enlarged generalized g…
math.OC2018
Partial smoothness and constant rank
Adrian S. Lewis, Jingwei Liang
The idea of partial smoothness in optimization blends certain smooth and nonsmooth properties of feasible regions and objective functions. As a consequence, the standard first-orde…