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Volumn 106, Issue 3, 2006, Pages 587-606

Minimizing polynomials via sum of squares over the gradient ideal

Author keywords

Algebraic Geometry; Global Optimization; Gradient Ideal; Polynomials; Radical Ideal; Semidefinite Programming (SDP); Sum of Squares (SOS); Variety

Indexed keywords

CONSTRAINT THEORY; GLOBAL OPTIMIZATION; GRADIENT METHODS; NUMERICAL METHODS; PROBLEM SOLVING;

EID: 33644502551     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-005-0672-6     Document Type: Article
Times cited : (155)

References (35)
  • 2
    • 0000913894 scopus 로고
    • The multidimensional moment problem and semi-groups
    • H.J. Landau (ed.), AMS, Providence, RI
    • Berg, C.: The multidimensional moment problem and semi-groups. In: Moments in Mathematics, H.J. Landau (ed.), AMS, Providence, RI, 1980, pp 110-124
    • (1980) Moments in Mathematics
    • Berg, C.1
  • 4
    • 33748567127 scopus 로고    scopus 로고
    • There are significantly more nonnegative polynomials than sums of squares
    • To appear
    • Blekherman, G.: There are significantly more nonnegative polynomials than sums of squares. To appear in Israel Journal of Mathematics
    • Israel Journal of Mathematics
    • Blekherman, G.1
  • 5
    • 0002083724 scopus 로고
    • Computation of real radicals of polynomial ideals
    • Computational algebraic geometry (Nice, 1992), Birkhäuser, Boston, MA
    • Becker, E., Neuhaus, R.: Computation of real radicals of polynomial ideals. Computational algebraic geometry (Nice, 1992), 1-20, Progress in Mathematics, 109, Birkhäuser, Boston, MA, 1993
    • (1993) Progress in Mathematics , vol.109 , pp. 1-20
    • Becker, E.1    Neuhaus, R.2
  • 6
    • 0031990029 scopus 로고    scopus 로고
    • Computation of real radicals of polynomial ideals. II
    • Becker, E., Neuhaus, R.: Computation of real radicals of polynomial ideals. II. J. Pure Appl. Algebra 124, 261-280 (1998)
    • (1998) J. Pure Appl. Algebra , vol.124 , pp. 261-280
    • Becker, E.1    Neuhaus, R.2
  • 7
    • 0003908675 scopus 로고    scopus 로고
    • Ideals, varieties and algorithms: An introduction to computational algebraic geometry and commutative algebra, second edition
    • Springer-Verlag, New York
    • Cox, D.A., Little, J.B., D.O'Shea.: Ideals, Varieties and Algorithms: an Introduction to Computational Algebraic Geometry and Commutative Algebra, Second Edition. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 1997
    • (1997) Undergraduate Texts in Mathematics
    • Cox, D.A.1    Little, J.B.2    O'Shea, D.3
  • 9
    • 0030682625 scopus 로고    scopus 로고
    • A reorder Schur factorization method for zero-dimensional polynomial systems with multiple roots
    • Maui, Hawaii
    • Corless, R.M., Gianni, P.M., Trager, B.M.: A reorder Schur factorization method for zero-dimensional polynomial systems with multiple roots. Proc. ACM Int. Symp. Symbolic and Algebraic Computation, Maui, Hawaii, 1997, pp 133-140
    • (1997) Proc. ACM Int. Symp. Symbolic and Algebraic Computation , pp. 133-140
    • Corless, R.M.1    Gianni, P.M.2    Trager, B.M.3
  • 10
    • 23044517911 scopus 로고    scopus 로고
    • The truncated complex K-moment problem
    • Curto, R.E., Fialkow, L.A.: The truncated complex K-moment problem. Trans. Am. Math. Soc. 352, 2825-2855 (2000)
    • (2000) Trans. Am. Math. Soc. , vol.352 , pp. 2825-2855
    • Curto, R.E.1    Fialkow, L.A.2
  • 12
    • 0036331337 scopus 로고    scopus 로고
    • Derivations and radicals of polynomial ideals over fields of arbitrary characteristic
    • Computer algebra (London, ON, 2001)
    • Fortuna, E., Gianni, P., Trager, B.: Derivations and radicals of polynomial ideals over fields of arbitrary characteristic. Computer algebra (London, ON, 2001). J. Symbolic Comput. 33 (5), 609-625 (2002)
    • (2002) J. Symbolic Comput. , vol.33 , Issue.5 , pp. 609-625
    • Fortuna, E.1    Gianni, P.2    Trager, B.3
  • 13
    • 85025493187 scopus 로고
    • Solving systems of polynomial inequalities in subexponential time
    • Grigoriev, D., Vorobjov, N. N., Jr. Solving systems of polynomial inequalities in subexponential time. J. Symbolic Comput. 5 (1-2), 37-64 (1988)
    • (1988) J. Symbolic Comput. , vol.5 , Issue.1-2 , pp. 37-64
    • Grigoriev, D.1    Vorobjov Jr., N.N.2
  • 14
    • 0042266229 scopus 로고    scopus 로고
    • Global minimization of a multivariate polynomial using matrix methods
    • Hanzon, B., Jibetean, D.: Global minimization of a multivariate polynomial using matrix methods. J. Global Optimization 27, 1-23 (2003)
    • (2003) J. Global Optimization , vol.27 , pp. 1-23
    • Hanzon, B.1    Jibetean, D.2
  • 16
    • 33947537644 scopus 로고    scopus 로고
    • Detecting global optimality and extracting solutions in GloptiPoly
    • Positive polynomials in control, D. Henrion, A. Garulli Eds., Springer, Berlin
    • Henrion, D., Lasserre, J.: Detecting global optimality and extracting solutions in GloptiPoly. Positive polynomials in control, D. Henrion, A. Garulli Eds., Lecture Notes on Control and Information Sciences, Vol. 312, Springer, Berlin, 2005, pp 293-310
    • (2005) Lecture Notes on Control and Information Sciences , vol.312 , pp. 293-310
    • Henrion, D.1    Lasserre, J.2
  • 18
    • 85030645974 scopus 로고
    • An algorithm for the computation of the radical of an ideal in the ring of polynomials
    • Applied algebra, algebraic algorithms and error-correcting codes (New Orleans, LA, 1991) Springer, Berlin
    • Krick, T., Logar, A.: An algorithm for the computation of the radical of an ideal in the ring of polynomials. Applied algebra, algebraic algorithms and error-correcting codes (New Orleans, LA, 1991), Lecture Notes in Comput. Sci., 539, Springer, Berlin, 1991, pp 195-205
    • (1991) Lecture Notes in Comput. Sci. , vol.539 , pp. 195-205
    • Krick, T.1    Logar, A.2
  • 19
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • Lasserre, J.: Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11 (3), 796-817 (2001)
    • (2001) SIAM J. Optim. , vol.11 , Issue.3 , pp. 796-817
    • Lasserre, J.1
  • 20
    • 33845284255 scopus 로고    scopus 로고
    • Semidefinite representations for finite varieties
    • To appear
    • Laurent, M.: Semidefinite representations for finite varieties. To appear in Mathematical Programming. Website: www.cwi.nl/~monique
    • Mathematical Programming
    • Laurent, M.1
  • 21
    • 0242541855 scopus 로고    scopus 로고
    • Optimization of polynomial functions
    • Marshall, M.: Optimization of polynomial functions. Canad. Math. Bull. 46, 575-587 (2003)
    • (2003) Canad. Math. Bull. , vol.46 , pp. 575-587
    • Marshall, M.1
  • 22
    • 0001776805 scopus 로고    scopus 로고
    • Squared functional systems and optimization problems
    • H. Frenk et al. (eds.), Kluwer Academic Publishers
    • Nesterov, Y.: Squared functional systems and optimization problems. High Performance Optimization H. Frenk et al. (eds.), Kluwer Academic Publishers, 2000, pp 405-440
    • (2000) High Performance Optimization , pp. 405-440
    • Nesterov, Y.1
  • 23
    • 33644523274 scopus 로고    scopus 로고
    • Minimum ellipsoid bounds for solutions of polynomial systems via sum of squares
    • to appear, arXiv:math.OC/0411122
    • Nie, J., Demmel, J. W.: Minimum ellipsoid bounds for solutions of polynomial systems via sum of squares, to appear in J. Global Optimization, arXiv:math.OC/0411122
    • J. Global Optimization
    • Nie, J.1    Demmel, J.W.2
  • 28
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite Programming relaxations for semialgebraic problems
    • Parrilo, P.: Semidefinite Programming relaxations for semialgebraic problems. Math. Program. Ser. B 96 (2), 293-320 (2003)
    • (2003) Math. Program. Ser. B , vol.96 , Issue.2 , pp. 293-320
    • Parrilo, P.1
  • 30
    • 1542296013 scopus 로고    scopus 로고
    • An explicit construction of distinguished representations of polynomials nonnegative over finite sets
    • March
    • Parrilo, P.: An explicit construction of distinguished representations of polynomials nonnegative over finite sets, If A Technical Report AUT02-02, March 2002
    • (2002) If A Technical Report , vol.AUT02-02
    • Parrilo, P.1
  • 31
    • 0000135301 scopus 로고
    • Positive polynomials on compact semi-algebraic sets
    • Putinar, M.: Positive polynomials on compact semi-algebraic sets. Ind. Univ. Math. J. 42, 203-206 (1993)
    • (1993) Ind. Univ. Math. J. , vol.42 , pp. 203-206
    • Putinar, M.1
  • 32
    • 0001572510 scopus 로고
    • On the computational complexity and geometry of the first-order theory of the reals. I-III
    • Renegar, J.: On the computational complexity and geometry of the first-order theory of the reals. I-III. J. Symbolic Comput. 13 (3), 255-352 (1992)
    • (1992) J. Symbolic Comput. , vol.13 , Issue.3 , pp. 255-352
    • Renegar, J.1
  • 33
    • 0001157581 scopus 로고    scopus 로고
    • th problem
    • American Mathematical Society
    • th problem. In Contemporary Mathematics, volume 253, American Mathematical Society, 2000, pp 251-272
    • (2000) Contemporary Mathematics , vol.253 , pp. 251-272
    • Reznick, B.1
  • 35
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite Programming
    • L. Vandenberghe and S. Boyd. Semidefinite Programming. SIAM Review 38, 49-95 (1996)
    • (1996) SIAM Review , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.