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arXiv · 1510.08577

The U-Lagrangian of a prox-regular function

Shuai Liu·Andrew Eberhard·Yousong Luo
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Abstract

When restricted to a subspace, a nonsmooth function can be differentiable. It is known that for a nonsmooth convex function f and a point x, the Euclidean space can be decomposed into two subspaces: U, over which a special Lagrangian can be defined and has nice smooth properties and V, the orthogonal complement subspace of U. In this paper we generalize the definition of UV-decomposition and U-Lagrangian to the context of nonconvex functions, specifically that of a prox-regular function.

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Shuai Liu, Andrew Eberhard, Yousong Luo. 2015-10-29. The U-Lagrangian of a prox-regular function. https://arxiv.org/abs/1510.08577

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