메뉴 건너뛰기




Volumn 47, Issue 2, 2012, Pages 167-191

Discriminants and nonnegative polynomials

Author keywords

Barrier; Discriminants; Hypersurface; Nonnegativity; Polynomials; Resultants; Semialgebraic sets; Varieties

Indexed keywords


EID: 81555228702     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2011.08.023     Document Type: Article
Times cited : (44)

References (31)
  • 4
    • 0003908675 scopus 로고    scopus 로고
    • Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra.
    • Springer, New York
    • Cox D., Little J., O'Shea D. Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. Undergraduate Texts in Mathematics 1997, Springer, New York. third edition.
    • (1997) Undergraduate Texts in Mathematics
    • Cox, D.1    Little, J.2    O'Shea, D.3
  • 6
    • 81555206510 scopus 로고    scopus 로고
    • Singular 3-1-3 - A computer algebra system for polynomial computations.
    • Decker, W., Greuel, G.-M., Pfister, G., Schönemann, H., 2011. Singular 3-1-3 - A computer algebra system for polynomial computations. http://www.singular.uni-kl.de.
    • (2011)
    • Decker, W.1    Greuel, G.-M.2    Pfister, G.3    Schönemann, H.4
  • 7
    • 0002106815 scopus 로고
    • On non-negative forms in real variables some or all of which are non-negative
    • Diananda P. On non-negative forms in real variables some or all of which are non-negative. Proc. Cambridge Philos. Soc. 1962, 58:17-25.
    • (1962) Proc. Cambridge Philos. Soc. , vol.58 , pp. 17-25
    • Diananda, P.1
  • 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. 2001, 11(3):796-817.
    • (2001) SIAM J. Optim. , vol.11 , Issue.3 , pp. 796-817
    • Lasserre, J.B.1
  • 12
    • 73249147288 scopus 로고    scopus 로고
    • Bi-Quadratic Optimization over Unit Spheres and Semidefinite Programming Relaxations
    • Ling C., Nie J., Qi L., Ye Y. Bi-Quadratic Optimization over Unit Spheres and Semidefinite Programming Relaxations. SIAM Journal on Optimization 2009, 20(3):1286-1310.
    • (2009) SIAM Journal on Optimization , vol.20 , Issue.3 , pp. 1286-1310
    • Ling, C.1    Nie, J.2    Qi, L.3    Ye, Y.4
  • 13
    • 20344396845 scopus 로고    scopus 로고
    • YALMIP: a toolbox for modeling and optimization in Matlab. In: Proc. IEEE CACSD Symposium, Taiwan.
    • Löfberg, J., 2004. YALMIP: a toolbox for modeling and optimization in Matlab. In: Proc. IEEE CACSD Symposium, Taiwan. http://www.control.isy.liu.se/~johanl.
    • (2004)
    • Löfberg, J.1
  • 14
    • 0003285762 scopus 로고
    • Isolated singular points on complete intersections
    • Cambridge University Press, Cambridge
    • Looijenga E. Isolated singular points on complete intersections. London Mathematical Society Lecture Note Series 1984, vol. 77. Cambridge University Press, Cambridge.
    • (1984) London Mathematical Society Lecture Note Series , vol.77
    • Looijenga, E.1
  • 15
    • 0001776805 scopus 로고    scopus 로고
    • Squared functional systems and optimization problems
    • Kluwer Academic Publishers, H. Frenk (Ed.)
    • Nesterov Yu. Squared functional systems and optimization problems. High Performance Optimization 2000, 405-440. Kluwer Academic Publishers. H. Frenk (Ed.).
    • (2000) High Performance Optimization , pp. 405-440
    • Nesterov, Y.1
  • 16
    • 33644502551 scopus 로고    scopus 로고
    • Minimizing polynomials via sum of squares over the gradient ideal
    • Nie J., Demmel J., Sturmfels B. Minimizing polynomials via sum of squares over the gradient ideal. Mathematical Programming Series A 2006, 106(3):587-606.
    • (2006) Mathematical Programming Series A , vol.106 , Issue.3 , pp. 587-606
    • Nie, J.1    Demmel, J.2    Sturmfels, B.3
  • 17
    • 70450198582 scopus 로고    scopus 로고
    • Algebraic degree of polynomial optimization
    • Nie J., Ranestad K. Algebraic degree of polynomial optimization. SIAM Journal on Optimization 2009, 20(1):485-502.
    • (2009) SIAM Journal on Optimization , vol.20 , Issue.1 , pp. 485-502
    • Nie, J.1    Ranestad, K.2
  • 18
    • 77954728894 scopus 로고    scopus 로고
    • Semidefinite Representation of the k-Ellipse
    • IMA 146, Springer, New York, A. Dickenstein, F.-O. Schreyer, A. Sommese (Eds.)
    • Nie J., Parrilo P., Sturmfels B. Semidefinite Representation of the k-Ellipse. Algorithms in Algebraic Geometry 2008, IMA Volume 146:117-132. Springer, New York. A. Dickenstein, F.-O. Schreyer, A. Sommese (Eds.).
    • (2008) Algorithms in Algebraic Geometry , pp. 117-132
    • Nie, J.1    Parrilo, P.2    Sturmfels, B.3
  • 21
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for semialgebraic problems
    • Parrilo P. Semidefinite programming relaxations for semialgebraic problems. Mathematical Programming Series B 2003, 96(2):293-320.
    • (2003) Mathematical Programming Series B , vol.96 , Issue.2 , pp. 293-320
    • Parrilo, P.1
  • 22
    • 2942687307 scopus 로고    scopus 로고
    • Minimizing polynomial functions
    • AMS, S. Basu, L. Gonzalez-Vega (Eds.) Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science
    • Parrilo P.A., Sturmfels B. Minimizing polynomial functions. DIMACS Series in Discrete Mathematics and Computer Science 2003, vol. 60:83-99. AMS. S. Basu, L. Gonzalez-Vega (Eds.).
    • (2003) DIMACS Series in Discrete Mathematics and Computer Science , vol.60 , pp. 83-99
    • Parrilo, P.A.1    Sturmfels, B.2
  • 23
    • 0000135301 scopus 로고
    • Positive polynomials on compact semi-algebraic sets
    • Putinar M. Positive polynomials on compact semi-algebraic sets. Ind. Univ. Math. J. 1993, 42:969-984.
    • (1993) Ind. Univ. Math. J. , vol.42 , pp. 969-984
    • Putinar, M.1
  • 24
    • 65249118802 scopus 로고    scopus 로고
    • A general formula for the algebraic degree in semidefinite programming
    • Ranestad K., Graf von Bothmer H.C. A general formula for the algebraic degree in semidefinite programming. Bulletin of LMS 2009, 41(2):193-197.
    • (2009) Bulletin of LMS , vol.41 , Issue.2 , pp. 193-197
    • Ranestad, K.1    Graf von Bothmer, H.C.2
  • 25
    • 81555220827 scopus 로고    scopus 로고
    • On the convex hull of a space curve, Advances in Geometry (in press).
    • Ranestad, K., Sturmfels, B., On the convex hull of a space curve, Advances in Geometry (in press).
    • Ranestad, K.1    Sturmfels, B.2
  • 26
    • 0001157581 scopus 로고    scopus 로고
    • Some concrete aspects of Hilbert's 17th problem
    • American Mathematical Society
    • Reznick B. Some concrete aspects of Hilbert's 17th problem. Contemp. Math. 2000, vol.~253:251-272. American Mathematical Society.
    • (2000) Contemp. Math. , vol.253 , pp. 251-272
    • Reznick, B.1
  • 27
    • 26444514585 scopus 로고    scopus 로고
    • On the absence of uniform denominators in Hilbert's seventeenth problem
    • Reznick B. On the absence of uniform denominators in Hilbert's seventeenth problem. Proceedings of the American Mathematical Society 2005, 133:2829-2834.
    • (2005) Proceedings of the American Mathematical Society , vol.133 , pp. 2829-2834
    • Reznick, B.1
  • 29
    • 0001250675 scopus 로고
    • The K-moment problem for compact semialgebraic sets
    • Schmüdgen K. The K-moment problem for compact semialgebraic sets. Math. Ann. 1991, 289:203-206.
    • (1991) Math. Ann. , vol.289 , pp. 203-206
    • Schmüdgen, K.1
  • 30
    • 0242632579 scopus 로고    scopus 로고
    • Solving systems of polynomial equations
    • American Mathematical Society, Providence, RI
    • Sturmfels B. Solving systems of polynomial equations. CBMS Regional Conference Series in Mathematics 2002, vol. 97. American Mathematical Society, Providence, RI.
    • (2002) CBMS Regional Conference Series in Mathematics , vol.97
    • Sturmfels, B.1
  • 31
    • 77958067804 scopus 로고    scopus 로고
    • Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
    • Sturmfels B., Uhler C. Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Annals of the Institute of Statistical Mathematics 2010, 62:603-638.
    • (2010) Annals of the Institute of Statistical Mathematics , vol.62 , pp. 603-638
    • Sturmfels, B.1    Uhler, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.