Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficiency of minimizing compositions of convex functions and smooth
  maps   We consider global efficiency of algorithms for minimizing a sum of a convex
function and a composition of a Lipschitz convex function with a smooth map.
The basic algorithm we rely on is the prox-linear method, which in each
iteration solves a regularized subproblem formed by linearizing the smooth map.
When the subproblems are solved exactly, the method has efficiency
$\mathcal{O}(\varepsilon^{-2})$, akin to gradient descent for smooth
minimization. We show that when the subproblems can only be solved by
first-order methods, a simple combination of smoothing, the prox-linear method,
and a fast-gradient scheme yields an algorithm with complexity
$\widetilde{\mathcal{O}}(\varepsilon^{-3})$. The technique readily extends to
minimizing an average of $m$ composite functions, with complexity
$\widetilde{\mathcal{O}}(m/\varepsilon^{2}+\sqrt{m}/\varepsilon^{3})$ in
expectation. We round off the paper with an inertial prox-linear method that
automatically accelerates in presence of convexity.

22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc