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A robust Lagrangian-DNN method for a class of quadratic optimization problems

Title
A robust Lagrangian-DNN method for a class of quadratic optimization problems
Authors
Arima, NaohikoKim, SunyoungKojima, MasakazuToh, Kim-Chuan
Ewha Authors
김선영
SCOPUS Author ID
김선영scopus
Issue Date
2017
Journal Title
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
ISSN
0926-6003JCR Link1573-2894JCR Link
Citation
vol. 66, no. 3, pp. 453 - 479
Keywords
Nonconvex quadratic optimization problems with nonnegative variablesThe Lagrangian-DNN relaxationImproved bisection methodThe validity of lower bounds
Publisher
SPRINGER
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
The Lagrangian-doubly nonnegative (DNN) relaxation has recently been shown to provide effective lower bounds for a large class of nonconvex quadratic optimization problems (QAPs) using the bisection method combined with first-order methods by Kim et al. (Math Program 156:161-187, 2016). While the bisection method has demonstrated the computational efficiency, determining the validity of a computed lower bound for the QOP depends on a prescribed parameter . To improve the performance of the bisection method for the Lagrangian-DNN relaxation, we propose a new technique that guarantees the validity of the computed lower bound at each iteration of the bisection method for any choice of . It also accelerates the bisection method. Moreover, we present a method to retrieve a primal-dual pair of optimal solutions of the Lagrangian-DNN relaxation using the primal-dual interior-point method. As a result, the method provides a better lower bound and substantially increases the robustness as well as the effectiveness of the bisection method. Computational results on binary QOPs, multiple knapsack problems, maximal stable set problems, and quadratic assignment problems illustrate the robustness of the proposed method. In particular, a tight bound for QAPs with size could be obtained.
DOI
10.1007/s10589-016-9879-0
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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