Sparsity in sums of squares of polynomials

被引：0
作者：
Masakazu Kojima
Sunyoung Kim
Hayato Waki
机构：
[1] Tokyo Institute of Technology,Department of Mathematical and Computing Sciences
[2] Ewha Women’s University,Department of Mathematics
来源：
Mathematical Programming | 2005年 / 103卷
关键词：
Sums of squares of polynomial; Polynomial optimization problem; Semidefinite program; Sparsity;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：45 / 62
页数：17
相关论文
共 13 条
  • [1] Choi J.F.(2)“SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones Proc. Symposia Pure Math. 58 103-653
  • [2] Kojima M.J.(2)“SDPT3 – a MATLAB software package for semidefinite programming, version 1.3” J. Operat. Res. Soc. Japan, 46 125-581
  • [3] Lasserre K.C.(2001)undefined SIAM J. Optimization 11 796-undefined
  • [4] Parrilo R. H.(2003)undefined Math. Programming 96 293-undefined
  • [5] Putinar undefined(1993)undefined Indiana Univ. Math. J. 42 969-undefined
  • [6] Powers undefined(1998)undefined J. Pure Appl. Algebra 127 99-undefined
  • [7] Reznick undefined(1978)undefined Duke Math. J. 45 363-undefined
  • [8] Reznick undefined(2000)undefined In Contemp. Math. 253 251-undefined
  • [9] Shor undefined(1987)undefined Cybernetics 23 731-undefined
  • [10] Strum undefined(1999)undefined Optimization Meth. Software 11 625-undefined
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