메뉴 건너뛰기




Volumn 106, Issue 1, 2006, Pages 93-109

Global optimization of rational functions: A semidefinite programming approach

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; MATHEMATICAL PROGRAMMING; POLYNOMIALS; PROBLEM SOLVING;

EID: 29144520191     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-005-0589-0     Document Type: Article
Times cited : (60)

References (24)
  • 1
    • 1842530967 scopus 로고    scopus 로고
    • Products of positive forms, linear matrix inequalities, and Hilbert 17-th problem for ternary forms
    • de Klerk, E., Pasechnik, D. V.: Products of positive forms, linear matrix inequalities, and Hilbert 17-th problem for ternary forms. European J. of Operational Research, 157 (1), 39-45 (2004)
    • (2004) European J. of Operational Research , vol.157 , Issue.1 , pp. 39-45
    • De Klerk, E.1    Pasechnik, D.V.2
  • 2
    • 0022010605 scopus 로고
    • CONOPT - A CRG code for large sparse dynamic nonlinear optimization problems
    • Drud, A.: CONOPT - a CRG code for large sparse dynamic nonlinear optimization problems. Mathematical Programming, 31, 153-191 (1985)
    • (1985) Mathematical Programming , vol.31 , pp. 153-191
    • Drud, A.1
  • 3
    • 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. Global Optimization, 27 (1), 1-23 (2003)
    • (2003) Global Optimization , vol.27 , Issue.1 , pp. 1-23
    • Hanzon, B.1    Jibetean, D.2
  • 4
    • 2542587541 scopus 로고    scopus 로고
    • Gloptipoly: Global optimization over polynomials with Matlab and SeDuMi
    • Henrion, D., Lasserre, J.: Gloptipoly: Global optimization over polynomials with Matlab and SeDuMi. ACM Transactions on Mathematical Software, 29 (2), 165-194, (2003)
    • (2003) ACM Transactions on Mathematical Software , vol.29 , Issue.2 , pp. 165-194
    • Henrion, D.1    Lasserre, J.2
  • 5
    • 29144509567 scopus 로고    scopus 로고
    • Global optimization of rational multivariate functions
    • CWI, Amsterdam
    • Jibetean, D.: Global optimization of rational multivariate functions. Technical Report PNA-R0120, CWI, Amsterdam, 2001
    • (2001) Technical Report , vol.PNA-R0120
    • Jibetean, D.1
  • 8
    • 0040214558 scopus 로고    scopus 로고
    • Cones of matrices and successive convex relaxations of nonconvex sets
    • Kojima, M., Tunçel, L.: Cones of matrices and successive convex relaxations of nonconvex sets. SIAM J. Optimization, 10, 750-778 (2000)
    • (2000) SIAM J. Optimization , vol.10 , pp. 750-778
    • Kojima, M.1    Tunçel, L.2
  • 9
    • 31844438920 scopus 로고    scopus 로고
    • Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization problems
    • Kojima, M., Tunçel, L.: Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization problems. Mathematical Programming. Series A, 89, 79-111 (2000)
    • (2000) Mathematical Programming. Series A , vol.89 , pp. 79-111
    • Kojima, M.1    Tunçel, L.2
  • 10
    • 0000052584 scopus 로고
    • An introduction to real algebra
    • Lam, T.: An introduction to real algebra. Rocky Mountain J. Math. 14 (4), 767-814 (1984)
    • (1984) Rocky Mountain J. Math. , vol.14 , Issue.4 , pp. 767-814
    • Lam, T.1
  • 11
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • Lassere, 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
    • Lassere, J.1
  • 12
    • 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. Optimization, 11, 296-817 (2001)
    • (2001) SIAM J. Optimization , vol.11 , pp. 296-817
    • Lasserre, J.1
  • 13
    • 0001776805 scopus 로고    scopus 로고
    • Squared functional systems and optimization problems
    • Frenk, H., Roos, K., Terlaky, T., Zhang, S. (eds). Kluwer Academic Publishers
    • Nesterov, Y.: Squared functional systems and optimization problems. In: Frenk, H., Roos, K., Terlaky, T., Zhang, S. (eds), High performance optimization, pages 405-440. Kluwer Academic Publishers, 2000
    • (2000) High Performance Optimization , pp. 405-440
    • Nesterov, Y.1
  • 15
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for semialgebraic problems
    • Parrilo, P. A. : Semidefinite programming relaxations for semialgebraic problems. Mathematical Programming Ser. B, 96 (2), 293-320 (2003)
    • (2003) Mathematical Programming Ser. B , vol.96 , Issue.2 , pp. 293-320
    • Parrilo, P.A.1
  • 17
    • 23044523312 scopus 로고    scopus 로고
    • Polynomials that are positive on an interval
    • Powers, V., Reznick, B.: Polynomials that are positive on an interval. Trans. Amer. Math. Soc. 352, 4677-4692 (2000)
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 4677-4692
    • Powers, V.1    Reznick, B.2
  • 19
    • 0000135301 scopus 로고
    • Positive polynomials on compact semi-algebraic sets
    • Putinar, M.: Positive polynomials on compact semi-algebraic sets. Ind. Univ. Math. J. 42, 969-984 (1993)
    • (1993) Ind. Univ. Math. J. , vol.42 , pp. 969-984
    • Putinar, M.1
  • 20
    • 51249169659 scopus 로고
    • Uniform denominators in Hilbert's seventeenth problem
    • Reznick, B.: Uniform denominators in Hilbert's seventeenth problem. Math. Z. 220 (1), 75-97 (1995)
    • (1995) Math. Z. , vol.220 , Issue.1 , pp. 75-97
    • Reznick, B.1
  • 21
    • 0001157581 scopus 로고    scopus 로고
    • Some concrete aspects of Hilbert's 17th problem
    • (Baton Rouge, LA). Amer. Math. Soc., Providence, RI
    • Reznick, B.: Some concrete aspects of Hilbert's 17th Problem. In: Real algebraic geometry and ordered structures (Baton Rouge, LA, 1996), pages 251-272. Amer. Math. Soc., Providence, RI, 2000
    • (1996) Real Algebraic Geometry and Ordered Structures , pp. 251-272
    • Reznick, B.1
  • 22
    • 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. 2, 203-206 (1991)
    • (1991) Math. Ann. , vol.2 , pp. 203-206
    • Schmüdgen, K.1
  • 23
    • 0242632579 scopus 로고    scopus 로고
    • Solving systems of polynomial equations
    • American Mathematical Society
    • Sturmfels, B.: Solving Systems of Polynomial Equations. Number 97 in CBMS Regional Conference Series in Mathematics. American Mathematical Society, 2002
    • (2002) CBMS Regional Conference Series in Mathematics , vol.97
    • Sturmfels, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.