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Volumn 89, Issue 5, 2007, Pages 399-403

A note on the representation of positive polynomials with structured sparsity

Author keywords

Positive polynomial; Sparse polynomial; Structured sparsity; Sum of squares

Indexed keywords


EID: 38649097540     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00013-007-2234-z     Document Type: Article
Times cited : (39)

References (12)
  • 1
    • 0000893882 scopus 로고
    • n et décomposition de polynômes à plusieurs variables.
    • n et décomposition de polynômes à plusieurs variables. J. Funct. Anal. 58, 254-266 (1984).
    • (1984) J. Funct. Anal , vol.58 , pp. 254-266
    • GASSIER, G.1
  • 2
    • 38649126805 scopus 로고    scopus 로고
    • M. KOJIMA AND M. MURAMATSU, A Note on Sparse SOS and SDP Relaxations for Polynomial Optimization Problems over Symmetric Cones. Research Report B-421, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology (2006). http://www.optimization-online.org/DB_HTML/2006/ 01/1292.html
    • M. KOJIMA AND M. MURAMATSU, A Note on Sparse SOS and SDP Relaxations for Polynomial Optimization Problems over Symmetric Cones. Research Report B-421, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology (2006). http://www.optimization-online.org/DB_HTML/2006/ 01/1292.html
  • 3
    • 51249193322 scopus 로고
    • Anneaux préordonnés.
    • J. KRIVINE, Anneaux préordonnés. J. Anal. Math. 12, 307-326 (1964).
    • (1964) J. Anal. Math , vol.12 , pp. 307-326
    • KRIVINE, J.1
  • 4
    • 38649134068 scopus 로고    scopus 로고
    • Positive polynomials on fibre products
    • preprint
    • S. KUHLMANN AND M. PUTINAR, Positive polynomials on fibre products, preprint.
    • KUHLMANN, S.1    PUTINAR, M.2
  • 5
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • J. B. LASSERRE, Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11, 796-817 (2001).
    • (2001) SIAM J. Optim , vol.11 , pp. 796-817
    • LASSERRE, J.B.1
  • 6
    • 34547492080 scopus 로고    scopus 로고
    • Convergent semidefinite relaxations in polynomial optimization with sparsity
    • J. B. LASSERRE, Convergent semidefinite relaxations in polynomial optimization with sparsity. SIAM J. Optim. 17, 822-843 (2006).
    • (2006) SIAM J. Optim , vol.17 , pp. 822-843
    • LASSERRE, J.B.1
  • 9
    • 0000135301 scopus 로고
    • Positive polynomials on compact semi-algebraic sets
    • M. PUTINAR, Positive polynomials on compact semi-algebraic sets. Indiana Univ. Math. J. 42(3), 969-984 (1993).
    • (1993) Indiana Univ. Math. J , vol.42 , Issue.3 , pp. 969-984
    • PUTINAR, M.1
  • 10
    • 0001250675 scopus 로고
    • The K-moment problem for compact semi-algebraic sets
    • K. SCHMÜDGEN, The K-moment problem for compact semi-algebraic sets. Math. Ann. 289, 203-206 (1991).
    • (1991) Math. Ann , vol.289 , pp. 203-206
    • SCHMÜDGEN, K.1
  • 11
    • 23844493105 scopus 로고    scopus 로고
    • Optimization of polynomials on compact semialgebraic sets
    • M. SCHWEIGHOFER, Optimization of polynomials on compact semialgebraic sets. SIAM J. Optim. 15(3), 805-825 (2005).
    • (2005) SIAM J. Optim , vol.15 , Issue.3 , pp. 805-825
    • SCHWEIGHOFER, M.1
  • 12
    • 33847158335 scopus 로고    scopus 로고
    • Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity
    • H. WAKI, S. KIM, M. KOJIMA, AND M. MURAMATSU, Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity. SIAM J. Optim. 17(1), 218-242 (2006).
    • (2006) SIAM J. Optim , vol.17 , Issue.1 , pp. 218-242
    • WAKI, H.1    KIM, S.2    KOJIMA, M.3    MURAMATSU, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.