BBCPOP swMATH ID: 31757 Software Authors: N. Ito, S. Kim, M. Kojima, A. Takeda, K.C. Toh Description: Algorithm 996: BBCPOP. The software package BBCPOP is a MATLAB implementation of a hierarchy of sparse doubly nonnegative (DNN) 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 DNN relaxation of the POP, and then solves the COP by applying the bisection and projection (BP) 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. Homepage: https://sites.google.com/site/bbcpop1/ Dependencies: Matlab Related Software: SDPNAL+; QAPLIB; SDPT3; GloptiPoly; SeDuMi; SCIP; BiqMac; Biq Mac; Matlab; Mosek; SparsePOP; SDPA; Sostools; Sparse-BSOS; ConicBundle; SPOTless; MIQCR-CB; ANTIGONE; MINLPLib; BARON Cited in: 7 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 996: BBCPOP: a sparse doubly nonnegative relaxation of polynomial optimization problems with binary, box, and complementarity constraints. Zbl 1486.65065Ito, Naoki; Kim, Sunyoung; Kojima, Masakazu; Takeda, Akiko; Toh, Kim-Chuan 2019 all top 5 Cited by 14 Authors 5 Kim, Sunyoung 4 Kojima, Masakazu 4 Toh, Kim Chuan 1 Azuma, Godai 1 Elloumi, Sourour 1 Fukuda, Mituhiro 1 Ito, Naoki 1 Lambert, Amélie 1 Lazare, Arnaud 1 Oliveira, Danilo Elias 1 Takeda, Akiko 1 Wolkowicz, Henry 1 Xu, Yangyang 1 Yamashita, Makoto Cited in 5 Serials 3 Journal of Global Optimization 1 ACM Transactions on Mathematical Software 1 Mathematical Programming. Series A. Series B 1 Optimization Methods & Software 1 Mathematical Programming Computation Cited in 2 Fields 6 Operations research, mathematical programming (90-XX) 1 Numerical analysis (65-XX) Citations by Year