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Volumn 42, Issue 1, 2009, Pages 31-41

A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones

Author keywords

Conic program; Euclidean Jordan algebra; Global optimization; Polynomial optimization problem; Semidefinite program; Sum of squares; Symmetric cone

Indexed keywords

ALGEBRA; OPTIMIZATION; POLYNOMIAL APPROXIMATION; POLYNOMIALS; SEMICONDUCTOR SWITCHES;

EID: 58149506266     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-007-9112-2     Document Type: Article
Times cited : (26)

References (13)
  • 3
    • 33244473532 scopus 로고    scopus 로고
    • Convergent relaxations of polynomial matrix inequalities and static output feedback
    • D. Henrion J.B. Lasserre 2006 Convergent relaxations of polynomial matrix inequalities and static output feedback IEEE Trans. Autom. Contr. 51 192 202
    • (2006) IEEE Trans. Autom. Contr. , vol.51 , pp. 192-202
    • Henrion, D.1    Lasserre, J.B.2
  • 5
    • 23844439934 scopus 로고    scopus 로고
    • Generalized Lagrangian duals and sums of squares relaxations of sparse polynomial optimization problems
    • S. Kim M. Kojima H. Waki 2005 Generalized Lagrangian duals and sums of squares relaxations of sparse polynomial optimization problems SIAM J. Optim. 15 697 719
    • (2005) SIAM J. Optim. , vol.15 , pp. 697-719
    • Kim, S.1    Kojima, M.2    Waki, H.3
  • 6
    • 17444428545 scopus 로고    scopus 로고
    • Sparsity in sums of squares of polynomials
    • M. Kojima S. Kim H. Waki 2005 Sparsity in sums of squares of polynomials Math. Program. 103 45 62
    • (2005) Math. Program. , vol.103 , pp. 45-62
    • Kojima, M.1    Kim, S.2    Waki, H.3
  • 8
    • 33947622683 scopus 로고    scopus 로고
    • An extension of sums of squares relaxations to polynomial optimization problems over symmetric cones
    • M. Kojima M. Muramatsu 2007 An extension of sums of squares relaxations to polynomial optimization problems over symmetric cones Math. Program. 110 315 336
    • (2007) Math. Program. , vol.110 , pp. 315-336
    • Kojima, M.1    Muramatsu, M.2
  • 9
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problems of moments
    • J.B. Lasserre 2007 Global optimization with polynomials and the problems of moments SIAM J. Optim. 11 796 817
    • (2007) SIAM J. Optim. , vol.11 , pp. 796-817
    • Lasserre, J.B.1
  • 10
    • 34547492080 scopus 로고    scopus 로고
    • Convergent SDP-relaxation in polynomial optimization with sparsity
    • J.B. Lasserre 2006 Convergent SDP-relaxation in polynomial optimization with sparsity SIAM J. Optim. 17 822 843
    • (2006) SIAM J. Optim. , vol.17 , pp. 822-843
    • Lasserre, J.B.1
  • 11
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for semialgebraic problems
    • P.A. Parrilo 2003 Semidefinite programming relaxations for semialgebraic problems Math. Program. 96 293 320
    • (2003) Math. Program. , vol.96 , pp. 293-320
    • Parrilo, P.A.1
  • 12
    • 0000135301 scopus 로고
    • Positive polynomials on compact semi-algebraic sets
    • M. Putinar 1993 Positive polynomials on compact semi-algebraic sets Indiana University Math. J. 42 969 984
    • (1993) Indiana University Math. J. , vol.42 , pp. 969-984
    • Putinar, M.1
  • 13
    • 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 M. Muramatsu 2006 Sums of squares and semidefinite programming relaxations for polynomial optimization problems with structured sparsity SIAM J. Optim. 17 218 242
    • (2006) SIAM J. Optim. , vol.17 , pp. 218-242
    • Waki, H.1    Kim, S.2    Kojima, M.3    Muramatsu, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.