Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On convexification/optimization of functionals including an l2-misfit
  term   We provide theory for computing the lower semi-continuous convex envelope of
functionals of the type f(x) plus an l2 misfit, and discuss applications to
various non-convex optimization problems. The latter term is a data fit term
whereas f provides structural constraints on x. By minimizing the above
expression, possibly with additional constraints, we thus find a tradeoff
between matching the measured data and enforcing a particular structure on x,
such as sparsity or low rank. For these particular cases, the theory provides
alternatives to convex relaxation techniques such as l1 -minimization (for
vectors) and nuclear norm-minimization (for matrices). For functionals where
the l2 misfit includes a singular matrix and where the convex envelope usually
is not explicitly computable, we provide theory for how minimizers of
(explicitly computable) approximations of the convex envelope relate to
minimizers of the original functional. In particular, we give explicit
conditions on when the two coincide.

29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol