Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strongly convex functions, Moreau envelopes and the generic nature of
  convex functions with strong minimizers   In this work, using Moreau envelopes, we define a complete metric for the set
of proper lower semicontinuous convex functions. Under this metric, the
convergence of each sequence of convex functions is epi-convergence. We show
that the set of strongly convex functions is dense but it is only of the first
category. On the other hand, it is shown that the set of convex functions with
strong minima is of the second category.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc