Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The U-Lagrangian of a prox-regular function   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.

37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th