3 research outputs found
A Difference-of-Convex Programming Approach With Parallel Branch-and-Bound For Sentence Compression Via A Hybrid Extractive Model
Sentence compression is an important problem in natural language processing
with wide applications in text summarization, search engine and human-AI
interaction system etc. In this paper, we design a hybrid extractive sentence
compression model combining a probability language model and a parse tree
language model for compressing sentences by guaranteeing the syntax correctness
of the compression results. Our compression model is formulated as an integer
linear programming problem, which can be rewritten as a Difference-of-Convex
(DC) programming problem based on the exact penalty technique. We use a
well-known efficient DC algorithm -- DCA to handle the penalized problem for
local optimal solutions. Then a hybrid global optimization algorithm combining
DCA with a parallel branch-and-bound framework, namely PDCABB, is used for
finding global optimal solutions. Numerical results demonstrate that our
sentence compression model can provide excellent compression results evaluated
by F-score, and indicate that PDCABB is a promising algorithm for solving our
sentence compression model.Comment: Full length paper (a short version of this paper for conference
proceedings can be found arXiv:1902.07248
Discrete Dynamical System Approaches For Boolean Polynomial Optimization
In this article, we discuss the numerical solution of Boolean polynomial
programs by algorithms borrowing from numerical methods for differential
equations, namely the Houbolt and Lie schemes, and a Runge-Kutta scheme. We
first introduce a quartic penalty functional (of Ginzburg-Landau type) to
approximate the Boolean program by a continuous one and prove some convergence
results as the penalty parameter converges to . We prove also
that, under reasonable assumptions, the distance between local minimizers of
the penalized problem and the (finite) set of solutions of the Boolean program
is of order . Next, we introduce algorithms for the numerical
solution of the penalized problem, these algorithms relying on the Houbolt, Lie
and Runge-Kutta schemes, classical methods for the numerical solution of
ordinary or partial differential equations. We performed numerical experiments
to investigate the impact of various parameters on the convergence of the
algorithms. Numerical tests on random generated problems show good performances
for our approaches. Indeed, our algorithms converge to local minimizers often
close to global minimizers of the Boolean program, and the relative
approximation error being of order .Comment: 29 pages, 30 figure
A Difference-of-Convex Cutting Plane Algorithm for Mixed-Binary Linear Program
In this paper, we propose a cutting plane algorithm based on DC
(Difference-of-Convex) programming and DC cut for globally solving Mixed-Binary
Linear Program (MBLP). We first use a classical DC programming formulation via
the exact penalization to formulate MBLP as a DC program, which can be solved
by DCA algorithm. Then, we focus on the construction of DC cuts, which serves
either as a local cut (namely type-I DC cut) at feasible local minimizer of
MBLP, or as a global cut (namely type-II DC cut) at infeasible local minimizer
of MBLP if some particular assumptions are verified. Otherwise, the
constructibility of DC cut is still unclear, and we propose to use classical
global cuts (such as the Lift-and-Project cut) instead. Combining DC cut and
classical global cuts, a cutting plane algorithm, namely DCCUT, is established
for globally solving MBLP. The convergence theorem of DCCUT is proved.
Restarting DCA in DCCUT helps to quickly update the upper bound solution and to
introduce more DC cuts for lower bound improvement. A variant of DCCUT by
introducing more classical global cuts in each iteration is proposed, and
parallel versions of DCCUT and its variant are also designed which use the
power of multiple processors for better performance. Numerical simulations of
DCCUT type algorithms comparing with the classical cutting plane algorithm
using Lift-and-Project cuts are reported. Tests on some specific samples and
the MIPLIB 2017 benchmark dataset demonstrate the benefits of DC cut and good
performance of DCCUT algorithms.Comment: 31 pages, 4 figure