Sparsity in sums of squares of polynomials

Authors:
Masakazu Kojima;Sunyoung Kim;Hayato Waki
Affiliations:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, 152-8552, Tokyo, Meguro-ku, Japan;Department of Mathematics, Ewha Women’s University, 11-1 Dahyun-dong, 120-750, Seoul, Sudaemoon-gu, Korea;Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, 152-8552, Tokyo, Meguro-ku, Japan
Venue:
Mathematical Programming: Series A and B
Year:
2005

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Abstract

Representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of sums of squares optimization and semidefinite programming (SDP) relaxation of polynomial optimization problems. We discuss effective methods to obtain a simpler representation of a “sparse” polynomial as a sum of squares of sparse polynomials by eliminating redundancy.