Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems

Sunyoung Kim () and Masakazu Kojima ()
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Sunyoung Kim: Ewha W. University
Masakazu Kojima: Tokyo Institute of Technology

Chapter Chapter 18 in Handbook on Semidefinite, Conic and Polynomial Optimization, 2012, pp 499-531 from Springer

Abstract: Abstract We present a survey on the sparse SDP relaxation proposed as a sparse variant of Lasserre’s SDP relaxation of polynomial optimization problems. We discuss the primal approach to derive the sparse SDP relaxation by exploiting the structured sparsity. In addition, numerical techniques used in the Matlab package SparsePOP for solving POPs are presented. We report numerical results on SparsePOP and the application of the sparse SDP relaxation to sensor network localization problems.

Keywords: Polynomial Optimization Problems (POP); Semidefinite Programming (SDP); SNL Problem; Schur Complement Matrix; Chordal Extension (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-1-4614-0769-0_18

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DOI: 10.1007/978-1-4614-0769-0_18

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