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Volumn 214, Issue 6, 2010, Pages 740-749

Semidefinite programming and sums of hermitian squares of noncommutative polynomials

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EID: 74149090510     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpaa.2009.07.003     Document Type: Article
Times cited : (18)

References (31)
  • 1
    • 0036761387 scopus 로고    scopus 로고
    • Positive noncommutative polynomials are sums of squares
    • Helton J.W. Positive noncommutative polynomials are sums of squares. Ann. of Math. (2) 156 2 (2002) 675-694
    • (2002) Ann. of Math. (2) , vol.156 , Issue.2 , pp. 675-694
    • Helton, J.W.1
  • 2
    • 18444414009 scopus 로고    scopus 로고
    • Noncommutative sums of squares
    • McCullough S., and Putinar M. Noncommutative sums of squares. Pacific J. Math. 218 1 (2005) 167-171
    • (2005) Pacific J. Math. , vol.218 , Issue.1 , pp. 167-171
    • McCullough, S.1    Putinar, M.2
  • 3
    • 74149088956 scopus 로고    scopus 로고
    • Engineering systems and free semi-algebraic geometry
    • Emerging Applications of Algebraic Geometry, Springer
    • de Oliveira M.C., Helton J.W., McCullough S., and Putinar M. Engineering systems and free semi-algebraic geometry. Emerging Applications of Algebraic Geometry. IMA Vol. Math. Appl. vol. 149 (2008), Springer 17-62
    • (2008) IMA Vol. Math. Appl. , vol.149 , pp. 17-62
    • de Oliveira, M.C.1    Helton, J.W.2    McCullough, S.3    Putinar, M.4
  • 4
    • 38149118947 scopus 로고    scopus 로고
    • Connes' embedding conjecture and sums of Hermitian squares
    • Klep I., and Schweighofer M. Connes' embedding conjecture and sums of Hermitian squares. Adv. Math. 217 4 (2008) 1816-1837
    • (2008) Adv. Math. , vol.217 , Issue.4 , pp. 1816-1837
    • Klep, I.1    Schweighofer, M.2
  • 5
    • 56349095426 scopus 로고    scopus 로고
    • Sums of Hermitian squares and the BMV conjecture
    • Klep I., and Schweighofer M. Sums of Hermitian squares and the BMV conjecture. J. Statist. Phys 133 4 (2008) 739-760
    • (2008) J. Statist. Phys , vol.133 , Issue.4 , pp. 739-760
    • Klep, I.1    Schweighofer, M.2
  • 6
    • 0000082954 scopus 로고
    • Sums of squares of real polynomials
    • K-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras. (Santa Barbara, CA, 1992), Amer. Math. Soc, Providence, RI
    • Choi M.D., Lam T.Y., and Reznick B. Sums of squares of real polynomials. K-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras. (Santa Barbara, CA, 1992). Proc. Sympos. Pure Math. vol. 58 (1995), Amer. Math. Soc, Providence, RI 103-126
    • (1995) Proc. Sympos. Pure Math. , vol.58 , pp. 103-126
    • Choi, M.D.1    Lam, T.Y.2    Reznick, B.3
  • 7
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for semialgebraic problems
    • Parrilo P.A. Semidefinite programming relaxations for semialgebraic problems. Math. Program. 96 2, Ser. B (2003) 293-320
    • (2003) Math. Program. , vol.96 , Issue.2 Ser. B , pp. 293-320
    • Parrilo, P.A.1
  • 9
    • 0011527172 scopus 로고
    • Academic Press Inc., New York
    • Rowen L.H. Polynomial Identities in Ring Theory. Pure and Applied Mathematics vol. 84 (1980), Academic Press Inc., New York
    • (1980) Pure and Applied Mathematics , vol.84
    • Rowen, L.H.1
  • 10
    • 33744916503 scopus 로고    scopus 로고
    • Springer-Verlag, Berlin Available from http://perso.univ-rennes1.fr/marie-francoise.roy/bpr-posted1.html
    • Basu S., Pollack R., and Roy M.-F. Algorithms in Real Algebraic Geometry. Algorithms and Computation in Mathematics vol. 10 (2006), Springer-Verlag, Berlin. http://perso.univ-rennes1.fr/marie-francoise.roy/bpr-posted1.html Available from http://perso.univ-rennes1.fr/marie-francoise.roy/bpr-posted1.html
    • (2006) Algorithms and Computation in Mathematics , vol.10
    • Basu, S.1    Pollack, R.2    Roy, M.-F.3
  • 13
    • 0031146175 scopus 로고    scopus 로고
    • An exact duality theory for semidefinite programming and its complexity implications
    • Ramana M.V. An exact duality theory for semidefinite programming and its complexity implications. Math. Program. 77 2, Ser. B (1997) 129-162
    • (1997) Math. Program. , vol.77 , Issue.2 Ser. B , pp. 129-162
    • Ramana, M.V.1
  • 14
    • 0003878614 scopus 로고    scopus 로고
    • Lectures on modern convex optimization
    • Analysis, Algorithms, and Engineering Applications, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • Ben-Tal A., and Nemirovski A. Lectures on modern convex optimization. Analysis, Algorithms, and Engineering Applications. MPS/SIAM Series on Optimization (2001), Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • (2001) MPS/SIAM Series on Optimization
    • Ben-Tal, A.1    Nemirovski, A.2
  • 15
    • 70450212537 scopus 로고    scopus 로고
    • Regularization methods for semi-definite programming
    • Malick J., Povh J., Rendl F., and Wiegele A. Regularization methods for semi-definite programming. SIAM J. Optim. 20 1 (2009) 336-356
    • (2009) SIAM J. Optim. , vol.20 , Issue.1 , pp. 336-356
    • Malick, J.1    Povh, J.2    Rendl, F.3    Wiegele, A.4
  • 16
    • 33751550994 scopus 로고    scopus 로고
    • A boundary point method to solve semidefinite programs
    • Povh J., Rendl F., and Wiegele A. A boundary point method to solve semidefinite programs. Computing 78 (2006) 277-286
    • (2006) Computing , vol.78 , pp. 277-286
    • Povh, J.1    Rendl, F.2    Wiegele, A.3
  • 17
    • 74149084090 scopus 로고    scopus 로고
    • 1 March 2009
    • H. Mittelman, http://plato.asu.edu/sub/pns.html, 1 March 2009
    • Mittelman, H.1
  • 18
    • 84972566433 scopus 로고
    • Extremal PSD forms with few terms
    • Reznick B. Extremal PSD forms with few terms. Duke Math. J. 45 2 (1978) 363-374
    • (1978) Duke Math. J. , vol.45 , Issue.2 , pp. 363-374
    • Reznick, B.1
  • 20
    • 0000920501 scopus 로고    scopus 로고
    • Semidefinite optimization
    • Todd M.J. Semidefinite optimization. Acta Numer. 10 (2001) 515-560
    • (2001) Acta Numer. , vol.10 , pp. 515-560
    • Todd, M.J.1
  • 21
    • 74149093311 scopus 로고    scopus 로고
    • 1 March 2009
    • SeDuMi, http://sedumi.ie.lehigh.edu/. 1 March 2009
    • SeDuMi
  • 22
    • 74149093722 scopus 로고    scopus 로고
    • K.-C. Toh, M.J. Todd, R.-H. Tütüncü, SDPT3 version 4.0 beta, a MATLAB software for semidefinite-quadratic-linear programming. Available from, 1 March 2009
    • K.-C. Toh, M.J. Todd, R.-H. Tütüncü, SDPT3 version 4.0 (beta) - a MATLAB software for semidefinite-quadratic-linear programming. Available from http://www.math.nus.edu.sg/~mattohkc/sdpt3.html, 1 March 2009
  • 23
    • 0001624064 scopus 로고    scopus 로고
    • Infeasible-start semidefinite programming algorithms via self-dual embeddings
    • Topics in Semidefinite and Interior-point Methods. (Toronto, ON, 1996), Amer. Math. Soc, Providence, RI
    • de Klerk E., Roos C., and Terlaky T. Infeasible-start semidefinite programming algorithms via self-dual embeddings. Topics in Semidefinite and Interior-point Methods. (Toronto, ON, 1996). Fields Inst. Commun. vol. 18 (1998), Amer. Math. Soc, Providence, RI 215-236
    • (1998) Fields Inst. Commun. , vol.18 , pp. 215-236
    • de Klerk, E.1    Roos, C.2    Terlaky, T.3
  • 24
    • 0001316562 scopus 로고    scopus 로고
    • On the complexity of semidefinite programs
    • Porkolab L., and Khachiyan L. On the complexity of semidefinite programs. J. Global Optim. 10 4 (1997) 351-365
    • (1997) J. Global Optim. , vol.10 , Issue.4 , pp. 351-365
    • Porkolab, L.1    Khachiyan, L.2
  • 25
    • 74149091665 scopus 로고    scopus 로고
    • K. Cafuta, I. Klep, J. Povh, NCSOStools: A computer algebra system for symbolic and numerical computation with noncommutative polynomials. Available from http://ncsostools.fis.unm.si/downloads/ncsostools_manual.pdf, 6 March 2009
    • K. Cafuta, I. Klep, J. Povh, NCSOStools: A computer algebra system for symbolic and numerical computation with noncommutative polynomials. Available from http://ncsostools.fis.unm.si/downloads/ncsostools_manual.pdf, 6 March 2009
  • 26
    • 74149092710 scopus 로고    scopus 로고
    • 1 March 2009
    • SOSTools, http://www.cds.caltech.edu/sostools/. 1 March 2009
    • SOSTools
  • 27
    • 0032064831 scopus 로고    scopus 로고
    • An algorithm for sums of squares of real polynomials
    • Powers V., and Wörmann T. An algorithm for sums of squares of real polynomials. J. Pure Appl. Algebra 127 1 (1998) 99-104
    • (1998) J. Pure Appl. Algebra , vol.127 , Issue.1 , pp. 99-104
    • Powers, V.1    Wörmann, T.2
  • 28
    • 74149084876 scopus 로고    scopus 로고
    • D. Henrion, J.-B. Lasserre, J. Löfberg, GloptiPoly 3: Moments, optimization and semidefinite programming. Available from http://www.laas.fr/~henrion/software/gloptipoly3/. 1 March 2009
    • D. Henrion, J.-B. Lasserre, J. Löfberg, GloptiPoly 3: Moments, optimization and semidefinite programming. Available from http://www.laas.fr/~henrion/software/gloptipoly3/. 1 March 2009
  • 29
    • 74149088883 scopus 로고    scopus 로고
    • YALMIP, 1 March 2009
    • YALMIP, http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php. 1 March 2009
  • 30
    • 20344396845 scopus 로고    scopus 로고
    • A toolbox for modeling and optimization in MATLAB
    • YALMIP:, Taipei, Taiwan
    • J. Löfberg, YALMIP: A toolbox for modeling and optimization in MATLAB, in: Proceedings of the CACSD Conference, Taipei, Taiwan, 2004
    • (2004) Proceedings of the CACSD Conference
    • Löfberg, J.1
  • 31
    • 33847158335 scopus 로고    scopus 로고
    • Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity
    • (electronic)
    • Waki H., Kim S., Kojima M., and Muramatsu M. Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity. SIAM J. Optim. 17 1 (2006) 218-242 (electronic)
    • (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.