Algorithm 883: SparsePOP - A sparse semidefinite programming relaxation of polynomial optimization problems

Hayato Waki; Sunyoung Kim; Masakazu Kojima; Masakazu Muramatsu; Hiroshi Sugimoto

doi:10.1145/1377612.1377619

Algorithm 883: SparsePOP - A sparse semidefinite programming relaxation of polynomial optimization problems

Hayato Waki
, Sunyoung Kim
, Masakazu Kojima
, Masakazu Muramatsu
, Hiroshi Sugimoto

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

111 Scopus citations

Abstract

SparsePOP is a Matlab implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki et al. [2006]. The sparse SDP relaxation exploits a sparse structure of polynomials in POPs when applying "a hierarchy of LMI relaxations of increasing dimensions" Lasserre [2006]. The efficiency of SparsePOP to approximate optimal solutions of POPs is thus increased, and larger-scale POPs can be handled.

Original language	English
Pages (from-to)	1-13
Number of pages	13
Journal	ACM Transactions on Mathematical Software
Volume	35
Issue number	2
DOIs	https://doi.org/10.1145/1377612.1377619
State	Published - 1 Jul 2008

Keywords

Global optimization
Matlab software package
Polynomial optimization problem
Semidefinite programming relaxation
Sparsity
Sums-of-squares optimization

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10.1145/1377612.1377619

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title = "Algorithm 883: SparsePOP - A sparse semidefinite programming relaxation of polynomial optimization problems",

abstract = "SparsePOP is a Matlab implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki et al. [2006]. The sparse SDP relaxation exploits a sparse structure of polynomials in POPs when applying {"}a hierarchy of LMI relaxations of increasing dimensions{"} Lasserre [2006]. The efficiency of SparsePOP to approximate optimal solutions of POPs is thus increased, and larger-scale POPs can be handled.",

keywords = "Global optimization, Matlab software package, Polynomial optimization problem, Semidefinite programming relaxation, Sparsity, Sums-of-squares optimization",

author = "Hayato Waki and Sunyoung Kim and Masakazu Kojima and Masakazu Muramatsu and Hiroshi Sugimoto",

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T2 - SparsePOP - A sparse semidefinite programming relaxation of polynomial optimization problems

AU - Waki, Hayato

AU - Kim, Sunyoung

AU - Kojima, Masakazu

AU - Muramatsu, Masakazu

AU - Sugimoto, Hiroshi

PY - 2008/7/1

Y1 - 2008/7/1

N2 - SparsePOP is a Matlab implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki et al. [2006]. The sparse SDP relaxation exploits a sparse structure of polynomials in POPs when applying "a hierarchy of LMI relaxations of increasing dimensions" Lasserre [2006]. The efficiency of SparsePOP to approximate optimal solutions of POPs is thus increased, and larger-scale POPs can be handled.

AB - SparsePOP is a Matlab implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki et al. [2006]. The sparse SDP relaxation exploits a sparse structure of polynomials in POPs when applying "a hierarchy of LMI relaxations of increasing dimensions" Lasserre [2006]. The efficiency of SparsePOP to approximate optimal solutions of POPs is thus increased, and larger-scale POPs can be handled.

KW - Global optimization

KW - Matlab software package

KW - Polynomial optimization problem

KW - Semidefinite programming relaxation

KW - Sparsity

KW - Sums-of-squares optimization

UR - https://www.scopus.com/pages/publications/48849097802

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DO - 10.1145/1377612.1377619

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SN - 0098-3500

VL - 35

SP - 1

EP - 13

JO - ACM Transactions on Mathematical Software

JF - ACM Transactions on Mathematical Software

IS - 2

ER -

Algorithm 883: SparsePOP - A sparse semidefinite programming relaxation of polynomial optimization problems

Abstract

Keywords

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