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Algorithm 996: BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems With Binary, Box, and Complementarity Constraints

Title
Algorithm 996: BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems With Binary, Box, and Complementarity Constraints
Authors
Ito, NaokiKim, SunyoungKojima, MasakazuTakeda, AkikoToh, Kim-Chuan
Ewha Authors
김선영
SCOPUS Author ID
김선영scopus
Issue Date
2019
Journal Title
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
ISSN
0098-3500JCR Link

1557-7295JCR Link
Citation
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE vol. 45, no. 3
Keywords
MATLAB software packagehigh-degree polynomial optimization problems with binarybox and complementarity constraintshierarchy of doubly nonnegative relaxationssparsitybisection and projection methodstight lower boundsefficiency
Publisher
ASSOC COMPUTING MACHINERY
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
The software package BBCPOP is a MATLAB implementation of a hierarchy of sparse doubly nonnegative relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box, and complementarity (BBC) constraints. Given a POP in the class and a relaxation order, BBCPOP constructs a simple conic optimization problem (COP), which serves as a doubly nonnegative relaxation of the POP, and then solves the COP by applying the bisection and projection method. The COP is expressed with a linear objective function and constraints described as a single hyperplane and two cones, which are the Cartesian product of positive semidefinite cones and a polyhedral cone induced from the BBC constraints. BBCPOP aims to compute a tight lower bound for the optimal value of a large-scale POP in the class that is beyond the comfort zone of existing software packages. The robustness, reliability, and efficiency of BBCPOP are demonstrated in comparison to the state-of-the-art software SDP package SDPNAL+ on randomly generated sparse POPs of degree 2 and 3 with up to a few thousands variables, and ones of degree from 5 to 8 with up to a few hundred variables. Numerical results on BBC-constrained POPs that arise from quadratic assignment problems are also reported. The software package BBCPOP is available at https://sites.google.com/sit/bbcpop1/.
DOI
10.1145/3309988
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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