Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General higher-order majorization-minimization algorithms for
  (non)convex optimization   Majorization-minimization algorithms consist of successively minimizing a
sequence of upper bounds of the objective function so that along the iterations
the objective function decreases. Such a simple principle allows to solve a
large class of optimization problems, even nonconvex and nonsmooth. We propose
a general higher-order majorization-minimization algorithmic framework for
minimizing an objective function that admits an approximation (surrogate) such
that the corresponding error function has a higher-order Lipschitz continuous
derivative. We present convergence guarantees for our new method for general
optimization problems with (non)convex and/or (non)smooth objective function.
For convex (possibly nonsmooth) problems we provide global sublinear
convergence rates, while for problems with uniformly convex objective function
we obtain locally faster superlinear convergence rates. We also prove global
stationary point guarantees for general nonconvex (possibly nonsmooth) problems
and under Kurdyka-Lojasiewicz property of the objective function we derive
local convergence rates ranging from sublinear to superlinear for our
majorization-minimization algorithm. Moreover, for unconstrained nonconvex
problems we derive convergence rates in terms of first- and second-order
optimality conditions.

15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn