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

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

102 Citations (Scopus)

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
Publication status	Published - Jul 1 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Software
Applied Mathematics

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10.1145/1377612.1377619

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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.",

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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.

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

Abstract

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