-
3
-
-
33745664818
-
The maximum likelihood degree
-
Catanese F., Hoşten S., Khetan A., Sturmfels B. The maximum likelihood degree. American Journal of Mathematics 2006, 128:671-697.
-
(2006)
American Journal of Mathematics
, vol.128
, pp. 671-697
-
-
Catanese, F.1
Hoşten, S.2
Khetan, A.3
Sturmfels, B.4
-
4
-
-
0003908675
-
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
-
-
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
-
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
-
8
-
-
0003353305
-
Discriminants, resultants, and multidimensional determinants
-
Birkhäuser
-
Gel'fand I., Kapranov M., Zelevinsky A. Discriminants, resultants, and multidimensional determinants. Mathematics: Theory & Applications 1994, Birkhäuser.
-
(1994)
Mathematics: Theory & Applications
-
-
Gel'fand, I.1
Kapranov, M.2
Zelevinsky, A.3
-
10
-
-
68949115889
-
GloptiPoly~3: moments, optimization and semidefinite programming
-
Henrion D., Lasserre J., Loefberg J. GloptiPoly~3: moments, optimization and semidefinite programming. Optimization Methods and Software 2009, vol.~24:761-779.
-
(2009)
Optimization Methods and Software
, vol.24
, pp. 761-779
-
-
Henrion, D.1
Lasserre, J.2
Loefberg, J.3
-
11
-
-
0035238864
-
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
-
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
-
-
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
-
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
-
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
-
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
-
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
-
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
-
20
-
-
69949110756
-
The algebraic degree of semidefinite programming
-
Nie J., Ranestad K., Sturmfels B. The algebraic degree of semidefinite programming. Mathematical Programming, Ser. A 2010, 122(2):379-405.
-
(2010)
Mathematical Programming, Ser. A
, vol.122
, Issue.2
, pp. 379-405
-
-
Nie, J.1
Ranestad, K.2
Sturmfels, B.3
-
21
-
-
1542266056
-
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
-
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
-
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
-
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
-
-
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
-
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
-
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
-
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
-
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
-
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
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