Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L_p$-norm regularization algorithms for optimization over permutation
  matrices   Optimization problems over permutation matrices appear widely in facility
layout, chip design, scheduling, pattern recognition, computer vision, graph
matching, etc. Since this problem is NP-hard due to the combinatorial nature of
permutation matrices, we relax the variable to be the more tractable doubly
stochastic matrices and add an $L_p$-norm ($0 < p < 1$) regularization term to
the objective function. The optimal solutions of the $L_p$-regularized problem
are the same as the original problem if the regularization parameter is
sufficiently large. A lower bound estimation of the nonzero entries of the
stationary points and some connections between the local minimizers and the
permutation matrices are further established. Then we propose an $L_p$
regularization algorithm with local refinements. The algorithm approximately
solves a sequence of $L_p$ regularization subproblems by the projected gradient
method using a nonmontone line search with the Barzilai-Borwein step sizes. Its
performance can be further improved if it is combined with certain local search
methods, the cutting plane techniques as well as a new negative proximal point
scheme. Extensive numerical results on QAPLIB and the bandwidth minimization
problem show that our proposed algorithms can often find reasonably high
quality solutions within a competitive amount of time.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci