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User Manual for BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems with Binary, Box and Complementarity Constraints

Naoki Ito (naoki_ito***at***mist.i.u-tokyo.ac.jp)
Sunyoung Kim (skim***at***ewha.ac.kr)
Masakazu Kojima (kojimamasakazu***at***mac.com)
Akiko Takeda (atakeda***at***ism.ac.jp)
Kim-Chuan Toh (mattohkc***at***nus.edu.sg)

Abstract: BBCPOP proposed in [4] 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 constraints. Given a POP in the class and a relaxation order (or a hierarchy level), 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 [6, 5]. The software package BBCPOP, this manual, and a test set of POPs are available at https://sites.google.com/site/bbcpop1/.

Keywords: Polynomial optimization problems, Doubly nonnegative relaxation, Bisection and projection method, Large-scale problems, MATLAB software package.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Linear, Cone and Semidefinite Programming (Other )

Category 3: Global Optimization

Citation: arXiv:1804.00761

Download: [PDF]

Entry Submitted: 04/02/2018
Entry Accepted: 04/02/2018
Entry Last Modified: 04/03/2018

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