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Sparsity in Sums of Squares of Polynomials

Masakazu Kojima (kojima***at***is.titech.ac.jp)
Sunyoung Kim (skim***at***ewha.ac.kr)
Hayato Waki (waki9***at***is.titech.ac.jp)

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 SDP (semidefinite programming) relaxation of polynomial optimization problems. We disscuss effective methods to obtain a simpler representation of a ``sparse'' polynomial as a sum of squares of sparse polynomials by eliminating redundancy.

Keywords: Sums of squares of polynomials, polynomial optimization problem, semidefinite program, sparsity

Category 1: Linear, Cone and Semidefinite Programming (Other )

Category 2: Combinatorial Optimization (Polyhedra )

Citation: Mathematical Programming Vol. 103 (2005) pp.45-62.


Entry Submitted: 09/29/2003
Entry Accepted: 09/29/2003
Entry Last Modified: 05/21/2005

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