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Volumn 166, Issue , 2012, Pages 1-22

Introduction to semidefinite, conic and polynomial optimization

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EID: 84940751969     PISSN: 08848289     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-4614-0769-0_1     Document Type: Chapter
Times cited : (83)

References (29)
  • 2
    • 33846667310 scopus 로고    scopus 로고
    • Reduction of symmetric semidefinite programs using the regular _-representation
    • de Klerk, E., Pasechnik, D. V., Schrijver, A.: Reduction of symmetric semidefinite programs using the regular _-representation. Math. Program. 109, 613-624 (2007)
    • (2007) Math. Program , vol.109 , pp. 613-624
    • de Klerk, E.1    Pasechnik, D.V.2    Schrijver, A.3
  • 3
    • 2942659750 scopus 로고    scopus 로고
    • Symmetry group, semidefinite programs and sums of squares
    • Gaterman, K., Parrilo, P.: Symmetry group, semidefinite programs and sums of squares. J. Pure Appl. Alg. 192, 95-128 (2004)
    • (2004) J. Pure Appl. Alg , vol.192 , pp. 95-128
    • Gaterman, K.1    Parrilo, P.2
  • 4
    • 84893574327 scopus 로고
    • Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
    • Goemans, M. X., Williamson, D. P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. Assoc. Comput. Mach. 42(6), 1115-1145 (1995)
    • (1995) J. Assoc. Comput. Mach , vol.42 , Issue.6 , pp. 1115-1145
    • Goemans, M.X.1    Williamson, D.P.2
  • 5
    • 0004236492 scopus 로고    scopus 로고
    • Johns Hopkins University Press, Baltimore, MD, third edition
    • Golub, G. H., Van Loan, C. F.: Matrix Computations. Johns Hopkins University Press, Baltimore, MD, third edition (1996)
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 7
    • 68949115889 scopus 로고    scopus 로고
    • Gloptipoly 3: Moments, optimization and semidefinite programming
    • Henrion, D., Lasserre, J. B., Lofberg, Y.: Gloptipoly 3: moments, optimization and semidefinite programming. Optim. Methods and Software 24, 761-779 (2009)
    • (2009) Optim. Methods and Software , vol.24 , pp. 761-779
    • Henrion, D.1    Lasserre, J.B.2    Lofberg, Y.3
  • 9
    • 51249193322 scopus 로고
    • Anneaux préordonnés
    • Krivine, J. L.: Anneaux préordonnés. J. Anal. Math. 12, 307-326 (1964)
    • (1964) J. Anal. Math , vol.12 , pp. 307-326
    • Krivine, J.L.1
  • 10
    • 84857636138 scopus 로고    scopus 로고
    • Semidefinite programming for min-max problems and games
    • Laraki, R., Lasserre, J. B.: Semidefinite programming for min-max problems and games. Math. Program. 1-28 http: //dx. doi. org/10. 1007/s10107-010-0353-y
    • Math. Program , pp. 1-28
    • Laraki, R.1    Lasserre, J.B.2
  • 11
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • Lasserre, J. B.: 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
  • 12
    • 18744415993 scopus 로고    scopus 로고
    • Polynomial programming: LP-relaxations also converge
    • Lasserre, J. B.: Polynomial programming: LP-relaxations also converge. SIAM J. Optim. 15, 383-393 (2004)
    • (2004) SIAM J. Optim , vol.15 , pp. 383-393
    • Lasserre, J.B.1
  • 13
    • 34547492080 scopus 로고    scopus 로고
    • Convergent SDP-relaxations in polynomial optimization with sparsity
    • Lasserre, J. B.: Convergent SDP-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
  • 15
    • 70450219137 scopus 로고    scopus 로고
    • Convexity in semi-algebraic geometry and polynomial optimization
    • Lasserre, J. B.: Convexity in semi-algebraic geometry and polynomial optimization. SIAM J. Optim. 19, 1995-2014 (2009)
    • (2009) SIAM J. Optim , vol.19 , pp. 1995-2014
    • Lasserre, J.B.1
  • 16
    • 0141517272 scopus 로고    scopus 로고
    • A comparison of the Sherali-Adams, Lovász-Schrijver and Lasserre relaxations for 0-1 programming
    • Laurent, M.: A comparison of the Sherali-Adams, Lovász-Schrijver and Lasserre relaxations for 0-1 programming. Math. Oper. Res. 28, 470-496 (2003)
    • (2003) Math. Oper. Res , vol.28 , pp. 470-496
    • Laurent, M.1
  • 17
    • 33745858905 scopus 로고    scopus 로고
    • Semidefinite programming and integer programming
    • Aardal, K., Nemhauser, G., Weismantel, R. (eds.), Elsevier
    • Laurent, M., Rendl, F.: Semidefinite programming and integer programming. In: Aardal, K., Nemhauser, G., Weismantel, R. (eds.) Handbook on Discrete Optimization, Elsevier (2005)
    • (2005) Handbook on Discrete Optimization
    • Laurent, M.1    Rendl, F.2
  • 18
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for semialgebraic problems
    • Parrilo, P. A.: Semidefinite programming relaxations for semialgebraic problems. Math. Program. Ser. B 96, 293-320 (2003)
    • (2003) Math. Program. Ser. B , vol.96 , pp. 293-320
    • Parrilo, P.A.1
  • 21
    • 0000135301 scopus 로고
    • Positive polynomials on compact semi-algebraic sets
    • Putinar, M.: Positive polynomials on compact semi-algebraic sets. Indiana Univ. Math. J. 42, 969-984 (1993)
    • (1993) Indiana Univ. Math. J , vol.42 , pp. 969-984
    • Putinar, M.1
  • 22
    • 52449148478 scopus 로고    scopus 로고
    • An exact duality theory for semidefinite programming and its complexity implications
    • Ser. B
    • Ramana, M. V.: An exact duality theory for semidefinite programming and its complexity implications. Math. Program., 77(2, Ser. B), 129-162 (1997)
    • (1997) Math. Program , vol.77 , Issue.2 , pp. 129-162
    • Ramana, M.V.1
  • 23
    • 0001250675 scopus 로고
    • The K-moment problem for compact semi-algebraic sets
    • Schmüdgen, K.: 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
  • 24
    • 23844493105 scopus 로고    scopus 로고
    • Optimization of polynomials on compact semialgebraic sets
    • Schweighofer, M.: Optimization of polynomials on compact semialgebraic sets. SIAM J. Optim. 15, 805-825 (2005)
    • (2005) SIAM J. Optim , vol.15 , pp. 805-825
    • Schweighofer, M.1
  • 25
    • 54149086891 scopus 로고    scopus 로고
    • Symmetry in semidefinite programs
    • Vallentin, F.: Symmetry in semidefinite programs. Linear Alg. Appl. 430, 360-369 (2009)
    • (2009) Linear Alg. Appl , vol.430 , pp. 360-369
    • Vallentin, F.1
  • 26
    • 33847158335 scopus 로고    scopus 로고
    • Sums of squares and semidefinite programming relaxations for polynomial optimization problems witth structured sparsity
    • Waki, S., Kim, S., Kojima, M., Maramatsu, M.: Sums of squares and semidefinite programming relaxations for polynomial optimization problems witth structured sparsity. SIAMJ. Optim. 17, 218-242 (2006)
    • (2006) SIAMJ. Optim , vol.17 , pp. 218-242
    • Waki, S.1    Kim, S.2    Kojima, M.3    Maramatsu, M.4
  • 27
    • 48849097802 scopus 로고    scopus 로고
    • SparsePOP: A Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems
    • Waki, H., Kim, S., Kojima, M., Muramatsu, M., Sugimoto, H.: SparsePOP: a Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems. ACM Trans. Math. Software 35(2), 15: 1-15: 13 (2008)
    • (2008) ACM Trans. Math. Software , vol.35 , Issue.2
    • Waki, H.1    Kim, S.2    Kojima, M.3    Muramatsu, M.4    Sugimoto, H.5
  • 28
    • 84867957035 scopus 로고    scopus 로고
    • Semidefinite programming for discrete optimization and matrix completion problems
    • Wolkowicz, H., Anjos, M. F.: Semidefinite programming for discrete optimization and matrix completion problems. Discrete Appl. Math., 123(1-2), 513-577 (2002)
    • (2002) Discrete Appl. Math , vol.123 , Issue.1-2 , pp. 513-577
    • Wolkowicz, H.1    Anjos, M.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.